www.wisdom.weizmann.ac.il
Open in
urlscan Pro
132.76.150.110
Public Scan
Submitted URL: http://www.wisdom.weizmann.ac.il//~fraenkel
Effective URL: https://www.wisdom.weizmann.ac.il/~fraenkel/
Submission: On August 03 via api from US — Scanned from IL
Effective URL: https://www.wisdom.weizmann.ac.il/~fraenkel/
Submission: On August 03 via api from US — Scanned from IL
Form analysis 0 forms found in the DOM
Text Content
AVIEZRI FRAENKEL'S HOME PAGE
This page lists some of my preprints, recent reprints, and indicates how to
access my Games Bibliography. Also my special favorite, the Responsa
Project,which is used worldwide, is mentioned briefly. It is a full text storage
and retrieval system, preceeding Google by 35 years. In 2007 it was awarded the
prestigious Israel Prize.
I. Some Preprints
II. English Reprints
III. Hebrew Transliterated Reprints
I. SOME PREPRINTS
* D.Klein and A.S.Fraenkel, K-Pile Wythoff Games, Lexicographic Wythoff, to
appear in Games Of No Chance.
* A.S. Fraenkel,Complementary balanced words over an arbitrary finite
https://link.springer.com/content/pdf/10.1007/s42979-024-02679-7.pdfalphabet.
* A.S. Fraenkel, lzichro shel Tzvi Betzer za"l, in Hebrew.
* A.S. Fraenkel, Tzadikim Urshaim b'mas' Horayot, in Hebrew. Preprint.
* A.S. Fraenkel, Leket Al Birkat Hachamah, in Hebrew. Preprint.
* A.S. Fraenkel, Hachodesh hazeh lachem
roshhttps://link.springer.com/content/pdf/10.1007/s42979-024-02679-7.pdf .
chodashim, in Hebrew. Preprint.
* A.S. Fraenkel, Ichud olamot, in Hebrew. Preprint.
* A.S. Fraenkel, Mah'peichat hamach'sheiv bcheikeir eitz haTorah, in Hebrew.
Preprint.
* A.S. Fraenkel, Tzvi Betzer Z"L -- gareis, dayeik v'yakir, in Hebrew.
Preprint.
II. ENGLISH REPRINTS
* O. Amir, A.Amir, A.S Fraenkel, D. Sarne, On the Practical Power of Automata
in Pattern Matching, Springer Nature Computer Science Journal, 6 April 2024.
* A.S. Fraenkel, Solomon W. Golomb's Enlightening Games, in: The Wisdom of
Solomon, The Genius and Legacy of Solomon Golomb, 165-168, 2023.
* A.S Fraenkel, Patrolling the Border of a Striking Conjecture, , INTEGERS,
Electr. J. Combinatorial Number Theory 22, 6pp, 2022
* A.S. Fraenkel and U. Larsson, Games on arbitrarily large rats and
playability, INTEGERS, Electr. J. Combinatorial Number Theory 19, 29pp,
2019.
* E. Duchene, A.S. Fraenkel, V. Gurvich, N.B. Ho, C. Kimberling and U. Larsson,
Wythoff Visions, In: Games of No Chance 5, Proc. BIRS Workshop on
Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (U. Larsson,
ed.), Vol. 70, Cambridge University Press, Cambridge, pp. 35--87, 2019.
* A.S. Fraenkel and U. Larsson, Take-away games on Beatty's Theorem and the
notion of k-invariance, In: Games of No Chance 5, Proc. BIRS Workshop on
Combinatorial Games, 2008, Banff, Alberta, Canada, MSRI Publ. (U. Larsson,
ed.), Vol. 70, Cambridge University Press, Cambridge, pp. 333--342, 2019. .
A.S. Fraenkel, U. Larsson, C. P. Santos & B. von Stengel, Editorial, Special
issue on combinatorial game theory, Intern. J. Game Theory, 47 no. 2 (2018)
375 - 377.
L. Goldberg and A.S. Fraenkel, Rulesets For Beatty Games, Intern. J. Game
Theory, special issue on combinatorial games. 47 no. 2 (2018) 577 - 594.
L. Goldberg and A.S. Fraenkel, Patterns in the generalized Fibonacci word,
applied to games, Discrete Math. 341 (2018) 1675-1687.
* H. Li, S. Liu and A.S. Fraenkel, Extensions and restrictions of generakized
Wythoff, 1--20.
H. Li, S. Liu, A.S. Fraenkel and W.A. Liu, Variants of $(s,t)$ Wythoff's
games, Discrete Appl. Math. 227 (2017) 1-12.
* G.E. Andrews, A.S. Fraenkel and J.A. Sellers, G.E. Andrews, A.S. Fraenkel and
J.A. Sellers, $m$-ary partitions with no gaps: a characterization modulo $m$,
Discrete Math. 339 (2016), pp. 283-287; DOI information:
* 10.1016/j.disc.2015.08.016 .
* A.S. Fraenkel, M. Rigo, Games derived from a generalized Thue-Morse word,
Intern. J. of Game Theory 1--13 (also in Combin. game theory colloq.
Abstract), 2016
*
* G.E. Andrews, A.S. Fraenkel and J.A. Sellers, Characterizing the number of
$m$-ary partitions modulo $m$, Amer. Math. Monthly, 122 (2015), no. 9,
880-885, 2015. Copyright November 2015 Mathematical Association of America.
All Rights Reserved.
A.S. Fraenkel and N.B. Ho, When are translati ons of P-positions of Wythoff's
game P-positions?, INTEGERS 15A, #A4, 12 pp., Proc. INTEGERS 2013 Conference,
The Erdos Centennial Conference, 2015.
F. Chung, C. Greene, J. Hutchinson -- Eds., Contributors; D.E. Knuth, A.S.
Fraenkel, D. Zeilberger, M. Petkovsek, N. Calkin, R. Canfield, A. Nijenhuis,
C.D. Savage, R.P. Stanley, F. Lazbenik -- Contributers,
Herbert S. Wilf (1931-2012) Remembrance, Notices AMS. vol. 62, No. 4,
346--360, April 2015. Full article at:
http://www.math.ucsd.edu/~fan/wilf/hw-ref.pdf .
A.S. Fraenkel and U. Peled, Harnessing the unwieldy MEX function, In: Games
of No Chance 4, Proc. BIRS Workshop on Combinatorial Games, 2008, Banff,
Alberta, Canada, MSRI Publ. (R.J. Nowakowski, ed.), Vol. 63, Cambridge
University Press, Cambridge, pp. 77--94, 2015.
A.S. Fraenkel, The Rat game and the Mouse game, In: Games of No Chance 4,
Proc. BIRS Workshop on Combinatorial Games, 2008, Banff, Alberta, Canada,
MSRI Publ. (R.J. Nowakowski, ed.), Vol. 63, Cambridge University Press,
Cambridge, pp. 95--113, 2015.
A.S. Fraenkel, R.A. Hearn and A.N. Siegel, Theory of combinatorial games,
Chapter 15 in: Handbook of Game Theory, Volume 4 (H. Peyton Young and Shmuel
Zamir, eds.), pp. 811- 859, Elsevier 2015.
A.S. Fraenkel, Integrating and Rejuvenating Old and New Gems, In Language,
Culture, Computation, Essayss Dedicated to Yaacov Choueka on the Occasion of
His 75th Birthday, Part I, pp. 37--49, Springer, 2014.
A. Fink, A.S. Fraenkel and C. Santos, Lim Is not Slim, Internat. J. Game
Theory (2014) 43:269-281 DOI 10.1007/s00182-013-0380-z
http://link.springer.com/article/10.1007%2Fs00182-013-0380-z#page-1.
A.S. Fraenkel, Beating Your Fractional Beatty Game Opponent and: What's the
Question to Your Answer? , in: Advances in Combinatorics, in Memory of
Herbert S. Wilf, Proc. Waterloo Workshop on Computer Algebra, I.S. Kotsireas
and E.V. Zima, eds., May 2011, pp. 175-186, Springer 2013.
A.S. Fraenkel and Y. Tanny, A Class of Wythoff-Like Games , Proc. INTEGERS
Conference, Carrollton, Georgia, Oct. 26-29, 2011, in: INTEGERS, Electr. J.
Combinat. Number Theory 12(B) (2013) #A7, 18pp. Also in Combinatorial Number
Theory, pp. 91-107, de Gruyter 2013. [Archive of INTEGERS.]
A.S. Fraenkel, Ratwyt, In memory of Martin Gardner, The College Math. J.,
March 2012, pp. 160-164.
A.S. Fraenkel, The vile, dopey, evil and odious game players, Discrete Math.
312 (2012) 42-46, special volume in honor of the 80th birthday of Gert
Sabidussi.
A.S. Fraenkel, Aperiodic subtraction games, Electronic J. Combinatorics vol.
18(2) P19 12pp., 2011. http://www.combinatorics.org/Journal/journalhome.html
S. Blanco and A.S. Fraenkel, Tromping Games: Tiling with Trominoes, Proc.
INTEGERS Conference, in honor of the birthdays of Melvyn Nathanson and Carl
Pomerance, Carrollton, Georgia, Oct. 14-17, 2009, in: INTEGERS, Electr. J.
Combinat. Number Theory 11(A) (2011) #6, 29pp.
U. Larsson, P. Hegarty and A.S. Fraenkel, Invariant and dual subtraction
games resolving the Duchene-Rigo conjecture, Theoretical Computer Science 412
(2011), 729-735.
A.S. Fraenkel, From enmity to amity. Amer. Math. Monthly 117 (2010),
646--648.
A.S. Fraenkel, Complementary Iterated Floor Words and the Flora Game. SIAM J.
on Discrete Math 24 (2010), 570--588.
E. Duchene, A.S. Fraenkel, R.J. Nowakowski and M. Rigo, Extensions and
restrictions of Wythoff's game preserving its P-positions. J. Combinat.
Theory A 117 (2010), 545--567.
J. Bell, E. Charlier, A.S. Fraenkel, M. Rigo, A decision problem for
ultimately periodic sets in non-standard numeration systems. Internat. J.
Algebra Computat 19 (2009), 6, 809--839.
A.S. Fraenkel and E. Reisner, The game of End-Wythoff, in Games of No Chance
3, Proc. BIRS Workshop on Combinatorial Games, July 2005, Banff, Alberta,
Canada, MSRI Publ. (M.H. Albert and R.J. Nowakowski, eds.), Vol. 56,
Cambridge University Press, Cambridge, pp. 329-347, 2009.
A.S. Fraenkel, The cyclic Butler University game, in: Mathematical Wizardry
for a Gardner (E. Pegg Jr, A.H. Schoen, and T. Rodgers, eds.), in honor of
Martin Gardner, pp. 97-105, A K Peters, Natick, MA, 2009.
E. Duchene, A.S. Fraenkel, S. Gravier and R.J. Nowakowski, Another bridge
between Nim and Wythoff, Australasian J. of Combinatorics 44 (2009), 43--56.
S. Artstein-Avidan, A.S. Fraenkel and V. Sos, A two-parameter family of an
extension of Beatty sequences, Discrete Math 308 (2008) 4578-4588.
A.S. Fraenkel, Games played by Boole and Galois, Discrete Appl. Math., 156
(2008) 420-427.
P.J. Davis and A.S. Fraenkel, Remembering Philip Rabinowitz, Notices AMS 54
(2007) 1502-1506. Reprinted, with the permission of the AMS, in The Birth of
Numerical Analysis (A. Bultheel, R. Cools, eds.) World Scientific (2009)
179-185.
A.S. Fraenkel, The Raleigh game. in: Combinatorial Number Theory, Proc.
INTEGERS Conference 2005, in celebration of the 70th birthday of Ronald
Graham, Carrollton, Georgia, Oct. 27-30, 2005; B. Landman, M. Nathanson, J.
Nesetril, R. Nowakowski, C. Pomerance, eds., de Gruyter, pp. 199-208, 2007.
Also appeared in INTEGERS, Electr. J. Combinat. Number Theory 7(2) (2007)
#13, 11pp., special volume in honor of Ron Graham.
A.S. Fraenkel and A. Kontorovich, The Sierpinski sieve of Nim-varieties and
binomial coefficients. in: Combinatorial Number Theory, Proc. Integers
Conference 2005, in celebration of the 70th birthday of Ronald Graham,
Carrollton, Georgia, Oct. 27-30, 2005; B. Landman, M. Nathanson, J. Nesetril,
R. Nowakowski, C. Pomerance, eds., de Gruyter, pp. 209-227, 2007. Also
appeared in INTEGERS, Electr. J. Combinat. Number Theory 7(2) (2007) #14,
19pp., special volume in honor of Ron Graham.
A.S. Fraenkel, Why are games exciting and stimulating?, Math Horizons
February 2007, 5--7; 32--33. A German translation, by Niek Neuwahl, was
poster-displayed at the ``Games & Science, Science & Games" exhibition, which
took place in Goettingen, July 17 -- Aug 21, 2005. It was selected as runner
up for an EMS Article Competition 2005 for the educated layman.
A.S. Fraenkel, Nim is easy, chess is hard --- but why??, J. Internat.
Computer Games Assoc. 29 (2006) 203--2006. Earlier shorter version appeared
in Plus Mag. (electronic) issue 40, pluschat section, Sept., 2006.
A.S. Fraenkel, Euclid and Wythoff games, Discrete Math. 304 (2005) 65--68.
Aviezri S. Fraenkel and Jamie Simpson, An extension of the periodicity lemma
to longer periods, Discrete Appl. Math. 146 (2005) 146-155 (special issue of
12th Annual Symposium on Combinatorial Pattern Matching). Preliminary version
appeared in Proc. 12th Annual Sympos. Combinatorial Pattern Matching,
Jerusalem, Israel, July 1--4, 2001 (A. Amir and G. M. Landau, eds.), Lecture
Notes in Computer Science, Springer, Berlin, pp. 98--105) (invited).
A.S. Fraenkel, New games related to old and new sequences. INTEGERS,
Electronic J. Combinat. Number Theory 4 (2004) #G06, 18pp.
http://www.integers-ejcnt.org . First version appeared in Advances in
Computer Games, Proc. 10-th Advances in Computer Games Conference (ACG-10),
Nov. 2003, Graz, Austria (H.J. van den Herik, H. Iida, E.A. Heinz, eds.), pp.
367--382, Kluwer.
A.S. Fraenkel, Complexity, appeal and challenges of combinatorial games,
Expanded version of a keynote address at Dagstuhl Seminar Feb.~17--22, 2002,
Theoretical Computer Science 313 (2004) 393-415, special issue on Algorithmic
Combinatorial Game Theory.
S.P. Fekete, R. Fleischer, A.S. Fraenkel and M. Schmitt, Traveling salesmen
in the presence of competition, Theoretical Computer Science 313 (2004)
377-392, special issue on Algorithmic Combinatorial Game Theory.
E.D. Demaine, R. Fleischer, A.S. Fraenkel and R.J. Nowakowski, Open problems
at the 2002 Dagstuhl Seminar on Algorithmic combinatorial game theory,
Theoretical Computer Science 313 (2004) 539-543, special issue on Algorithmic
Combinatorial Game Theory (Appendix B).
A.S. Fraenkel and Dalia Krieger, The structure of complementary sets of
integers: a 3-shift theorem, Internat. J. Pure and Appl. Math. 10 (2004)
1--49.
Aviezri S. Fraenkel and Ofer Rahat, Complexity of error-correcting codes
derived from combinatorial games, Proc. Intern. Conference on Computers and
Games CG'2002, Edmonton, Alberta, Canada, July 2002 (Y. Bj\"{o}rnsson, M.\
M\"{u}ller, J. Schaeffer, eds.), Lecture Notes in Computer Science LNCS 2883,
pp. 201--212, Springer 2003.
Aviezri S. Fraenkel, Jamie Simpson and Mike Paterson, On abelian circular
squares in binary words. In: Paul Erdos and his Mathematics II, Bolyai Soc.,
Mathematical Studies 11, Budapest 2002, pp. 329--338. An earlier version
entitled ``On weak circular squares in binary words'' appeared in Proc. 8th
Annual Symposium on Combinatorial Pattern Matching, Aarhus, Denmark, June
30--July 2, 1997 (A. Apostolico and J. Hein, eds.), Lecture Notes in Computer
Science, Springer, Berlin, pp. 76--82).
A.S. Fraenkel, Two-player games on cellular automata, in More Games of No
Chance, Proc. MSRI Workshop on Combinatorial Games, July 10--28, 2000,
Berkeley, CA (R. J. Nowakowski, ed.), Cambridge University Press, Cambridge,
Vol. 42, 2002, pp. 279--306.
A.S. Fraenkel, Arrays, numeration systems and Frankenstein games, Theoretical
Computer Science 282 (2002) 271--284 (special "FUN in Algorithms" issue).
A.S. Fraenkel, Mathematical Chats Between Two Physicists, in Puzzlers'
Tribute: A Feast for the Mind, honoring Martin Gardner (D. Wolfe and T.
Rodgers, eds.), A K Peters, 2002, pp. 315--325.
A.S. Fraenkel, Virus versus mankind, in: Proc. 2nd Intern. Conference on
Computer Games CG'2000, Hamamatsu, Japan, Oct. 2000, Lecture Notes in
Computer Science, Springer (T. Marsland, I. Frank, eds.), 2001, pp. 204--213.
A.S. Fraenkel, T. Seeman and J. Simpson The subword complexity of a
two-parameter family of sequences, Electronic J. Combinatorics vol. 8(2) R10,
2001 http://www.combinatorics.org/Journal/journalhome.html
A.S. Fraenkel, A Selection Of Mathematical Board Games, Abstract Presented at
Board Games in Academia III, Florence, April 12--15, 1999. Proceedings Board
Games in Academia III, pp. 46--67.
A.S. Fraenkel and D. Zusman, A New Heap Game, Theoretical Computer Science
252 (2001) 5--12 (special "Computers and Games issue"). Initial version
appeared in Lecture Notes in Computer Science 1558, Proc. 1-st Intern.
Conference on Computer Games, Tsukuba, Japan, Nov. 1998, pp. 205--211, 1999.
A.S. Fraenkel and O. Rahat, Infinite cyclic impartial games, Theoretical
Computer Science 252 (2001) 13-22 (special "Computers and Games issue").
Initial version appeared in Lecture Notes in Computer Science 1558, Proc.
1-st Intern. Conference on Computer Games, Tsukuba, Japan, Nov. 1998, pp.
212--221, 1999.
A.S. Fraenkel, Recent results and questions in combinatorial game
complexities, Expanded version of invited lecture at Ninth Australasian
Workshop on Combinatorial Algorithms, Perth, Western Australia, 27---30 July
1998, Theoret. Comput. Sci. 249 (2000) 265--288. Conference version in: Proc.
AWOCA98 --- Ninth Australasian Workshop on Combinatorial Algorithms, (C.S.
Iliopoulos, ed.), pp. 124--146.
A.S. Fraenkel, On the recurrence f(m+1)=b(m)f(m)-f(m-1) and applications,
Discrete Mathematics 224 (2000) 273--279 (Note).
A.S. Fraenkel and S.T. Klein, Information retrieval from annotated texts, J.
Amer. Soc. for Information Sciences 50 (1999) 845--854.
A.S. Fraenkel and Jamie Simpson, The exact number of squares in Fibonacci
words, Theoret. Comput. Sci. 218 (1999) 95--106 (special Words issue).
A.S. Fraenkel, Protein folding, spin glass and computational complexity,
Expanded form of invited paper presented at DNA Based Computers III, Proc.
DIMACS Workshop (H. Rubin and D. H. Wood, Eds.), June 23--25, 1997,
University of Pennsylvania, DIMACS Series in Discrete Mathematics and
Theoretical Computer Science Vol. 48, AMS, 1999, pp. 101--121.
A.S. Fraenkel, Heap games, numeration systems and sequences, Annals of
Combinatorics 2 (1998) 197--210.
U.Blass, A.S. Fraenkel and R. Guelman, How far can Nim in disguise be
stretched?, J. Combin. Theory (Ser. A) 84 (1998) 145--156.
A.S. Fraenkel, The Responsa storage and retrieval system---whither? The
Hebrew version: Proyect hashut: avar, hoveh---v'gam atid? appeared in Dinei
Yisrael 19 (1997-98) 253--270.
A.S. Fraenkel and Michal Ozery, Adjoining to Wythoff's game its P-positions
as moves, Theoretical Computer Science 205 (1998) 283--296.
A.S. Fraenkel, Multivision: a game of arbitrarily long play, Amer. Math.
Monthly 105 (1998) 923--928.
A.S. Fraenkel and Jamie Simpson, How many squares can a string contain? J.
Combin. Theory Ser. A 82 (1998) 112--120. Errata: In Table 1, the number of
maximal words (last column) should be 6 and 72 for n=3 and n=12 respectively.
These corrections do not otherwise affect the results of the paper. We thank
Troy Vasiga for pointing out the first of these typos.
* A.S. Fraenkel, Systems of numeration, AMM 1985, 105--114.
* A.S. Fraenkel and D. Lichtenstein, Computing a perfect strategy for n x n
chess requires time exponential in n, J. Combin. Theory Ser. A 31 (1981)
1 99--214..
* M. Boshernitzan and A.S. Fraenkel, Nonhomogenious spectra of numbers,
Discrete Math., Communication (1981) 325--327/
* A.S. Fraenkel, Combinatorial game theory foundations applied to digraph
kernels , Electronic J. of Combinatorics 4(2) (1997) R10, 17pp. (Wilf
Festschrift).
A.S. Fraenkel,
and S.Simonson,
Geography.
Theoretical Comput. Sci.
110
(1993),
no. 1,
197–214.
M.A.
Berger,
A.
Felzenbaum,
A.S.Fraenkel
and R.
Holzman,
On infinite and finite covering systems.
Amer. Math. Monthly
98
(1991),
no. 8,
739–742.
M.A. Berger,
A. Felzenbaum
asnd
Fraenkel, Aviezri S.
Irreducible disjoint covering systems (with an application to Boolean
algebra).
First International Colloquium on Pseudo-Boolean Optimization and Related
Topics (Chexbres, 1987).
Discrete Appl. Math.
29
(1990),
no. 2-3,
143–164.
MR4363103 Reviewed Fraenkel, Aviezri S. Patrolling the border of a striking
conjecture. Integers 22 (2022), Paper No. A3, 6 pp. 11B75
Review PDF Clipboard Journal Article
MR4188748 Reviewed Fraenkel, Aviezri S.; Larsson, Urban Games on arbitrarily
large rats and playability. Integers 19 (2019), Paper No. G04, 29 pp.
(Reviewer: Grant Cairns) 91A46 (05A17 11B75)
Review PDF Clipboard Journal Article 3 Citations
MR3965376 Reviewed Fraenkel, Aviezri S.; Larsson, Urban Take-away games on
Beatty's theorem and the notion of k-invariance. Games of no chance
5, 333–342, Math. Sci. Res. Inst. Publ., 70, Cambridge Univ. Press,
Cambridge, 2019. 91A46
Review PDF Clipboard Series Chapter 1 Citation
MR3965364 Reviewed Duch�ne, Eric; Fraenkel, Aviezri S.; Gurvich,
Vladimir; Ho, Nhan Bao; Kimberling, Clark; Larsson, Urban Wythoff
visions. Games of no chance 5, 35–87, Math. Sci. Res. Inst. Publ.,
70, Cambridge Univ. Press, Cambridge, 2019. 91A46 (91-02)
Review PDF Clipboard Series Chapter 5 Citations
MR3842044 Reviewed Goldberg, Lior; Fraenkel, Aviezri S. Rulesets for Beatty
games. Internat. J. Game Theory 47 (2018), no. 2, 577–594. 91A46
Review PDF Clipboard Journal Article 1 Citation
MR3842035 Indexed Fraenkel, Aviezri; Larsson, Urban; Santos, Carlos P.; von
Stengel, Bernhard Special issue on combinatorial game theory. Internat. J.
Game Theory 47 (2018), no. 2, 375–377. 91-06 (91A46)
Review PDF Clipboard Journal Article
MR3784788 Reviewed Goldberg, Lior; Fraenkel, Aviezri S. Patterns in the
generalized Fibonacci word, applied to games. Discrete Math. 341 (2018), no.
6, 1675–1687. 68R15 (91A46)
Review PDF Clipboard Journal Article
MR3661410 Reviewed Li, Haiyan; Liu, Sanyang; Fraenkel, Aviezri S.; Liu, Wen
An Variants of (s,t)-Wythoff's game. Discrete Appl. Math. 227 (2017), 1–12.
(Reviewer: Grant Cairns) 91A46
Review PDF Clipboard Journal Article 2 Citations
MR3404489 Reviewed Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James
A. m-ary partitions with no gaps: a characterization modulo m. Discrete
Math. 339 (2016), no. 1, 283–287. 05A17 (05A15 11P81)
Review PDF Clipboard Journal Article 5 Citations
MR3560331 Reviewed Fraenkel, Aviezri S. The Rat game and the Mouse
game. Games of no chance 4, 95–113, Math. Sci. Res. Inst. Publ.,
63, Cambridge Univ. Press, New York, 2015. 91A46
Review PDF Clipboard Series Chapter 8 Citations
MR3560330 Reviewed Fraenkel, Aviezri S.; Peled, Udi Harnessing the unwieldy
MEX function. Games of no chance 4, 77–94, Math. Sci. Res. Inst. Publ.,
63, Cambridge Univ. Press, New York, 2015. (Reviewer: Grant Cairns) 91A46
Review PDF Clipboard Series Chapter 10 Citations
MR3418210 Reviewed Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James
A. Characterizing the number of m-ary partitions modulo m. Amer. Math.
Monthly 122 (2015), no. 9, 880–885. (Reviewer: David M. Bressoud) 05A17
(11P83)
Review PDF Clipboard Journal Article 9 Citations
MR3361813 Reviewed Fraenkel, Aviezri S.; Ho, Nhan Bao When are translations
of P-positions of Wythoff's game P-positions? Integers 15A (2015), Paper No.
A4, 12 pp. (Reviewer: Paweł Prałat) 91A46 (91A05)
Review PDF Clipboard Journal Article 3 Citations
MR3233468 Indexed Fraenkel, Aviezri S.; Simpson, Jamie Corrigendum to "The
exact number of squares in Fibonacci words'' [Theoret. Comput. Sci. 218 (1)
(1999) 95–106] [MR1687768]. Theoret. Comput. Sci. 547 (2014), 122. 68R15
(11B39)
Review PDF Clipboard Journal Article 1 Citation
MR3197293 Reviewed Fink, Alex; Fraenkel, Aviezri S.; Santos, Carlos LIM is
not slim. Internat. J. Game Theory 43 (2014), no. 2, 269–281. (Reviewer: Nhan
Bao Ho) 91A46 (68Q80)
Review PDF Clipboard Journal Article 1 Citation
MR3363969 Reviewed Fraenkel, Aviezri S. Beating your fractional Beatty game
opponent and: what's the question to your answer? Advances in
combinatorics, 175–186, Springer, Heidelberg, 2013. (Reviewer: Nhan Bao
Ho) 91A46
Review PDF Clipboard Series Chapter 2 Citations
MR3220917 Indexed Fraenkel, Aviezri S.; Tanny, Yuval A class of Whythoff-like
games [reprint of MR3055681]. Combinatorial number theory, 91–107, De Gruyter
Proc. Math., De Gruyter, Berlin, 2013. 91A46
Review PDF Clipboard Series Chapter
MR3055681 Reviewed Fraenkel, Aviezri; Tanny, Yuval A class of Wythoff-like
games. Integers 12B (2012/13), Proceedings of the Integers Conference
2011, Paper No. A7, 18 pp. (Reviewer: Nhan Bao Ho) 91A46
Review PDF Clipboard Journal Article 6 Citations
MR2897480 Reviewed Fraenkel, Aviezri S. RATWYT. College Math.
J. 43 (2012), no. 2, 160–164. 91A46 (11B75 91A26)
Review PDF Clipboard Journal Article 1 Citation
MR2852506 Indexed Fraenkel, Aviezri S. The vile, dopey, evil and odious game
players. Discrete Math. 312 (2012), no. 1, 42–46. 91A46
Review PDF Clipboard Journal Article 7 Citations
MR2988066 Reviewed Blanco, Sa�l A.; Fraenkel, Aviezri S. Tromping games:
tiling with trominoes. Integers 11 (2011), no. 3, 333–362. (Reviewer: Grant
Cairns) 91A46 (05B50)
Review PDF Clipboard Journal Article
MR2830984 Reviewed Fraenkel, Aviezri S. Aperiodic subtraction
games. Electron. J. Combin. 18 (2011), no. 2, Paper 19, 12 pp. (Reviewer:
Peter Vincent Hegarty) 91A46 (11B75 68Q25 91A05)
Review PDF Clipboard Journal Article 11 Citations
MR2796920 Reviewed Larsson, Urban; Hegarty, Peter; Fraenkel, Aviezri
S. Invariant and dual subtraction games resolving the Duch�ne-Rigo
conjecture. Theoret. Comput. Sci. 412 (2011), no. 8-10, 729–735. (Reviewer:
Andr�s S�ndor Pluh�r) 91A46
Review PDF Clipboard Journal Article 9 Citations
MR2681526 Indexed Fraenkel, Aviezri S. From enmity to amity. Amer. Math.
Monthly 117 (2010), no. 7, 646–648. 11B83
Review PDF Clipboard Journal Article 2 Citations
MR2661423 Reviewed Fraenkel, Aviezri S. Complementary iterated floor words
and the Flora game. SIAM J. Discrete Math. 24 (2010), no. 2, 570–588.
(Reviewer: E. J. Barbeau) 91A46 (05A05 11B75)
Review PDF Clipboard Journal Article 5 Citations
MR2604147 Indexed Davis, Philip J.; Fraenkel, Aviezri S. Remembering Philip
Rabinowitz [reprint of MR2361163]. The birth of numerical
analysis, 179–186, World Sci. Publ., Hackensack, NJ, 2010. 65-03 (01A70
65D30)
Review PDF Clipboard Series Chapter
MR2600974 Reviewed Duch�ne, Eric; Fraenkel, Aviezri S.; Nowakowski, Richard
J.; Rigo, Michel Extensions and restrictions of Wythoff's game preserving
its P positions. J. Combin. Theory Ser. A 117 (2010), no. 5, 545–567.
(Reviewer: Thane Earl Plambeck) 91A46 (91A43)
Review PDF Clipboard Journal Article 33 Citations
MR2572876 Reviewed Bell, Jason; Charlier, Emilie; Fraenkel, Aviezri S.; Rigo,
Michel A decision problem for ultimately periodic sets in nonstandard
numeration systems. Internat. J. Algebra Comput. 19 (2009), no. 6, 809–839.
(Reviewer: Petr Ambrož) 68Q45 (03B25 11B85 11U05)
Review PDF Clipboard Journal Article 5 Citations
MR2526997 Reviewed Duch�ne, E.; Fraenkel, A. S.; Gravier, S.; Nowakowski, R.
J. Another bridge between NIM and WYTHOFF. Australas. J.
Combin. 44 (2009), 43–56. (Reviewer: Thane Earl Plambeck) 91A46
Review PDF Clipboard Journal Article 17 Citations
MR2438162 Reviewed Artstein-Avidan, Shiri; Fraenkel, Aviezri S.; S�s, Vera
T. A two-parameter family of an extension of Beatty sequences. Discrete
Math. 308 (2008), no. 20, 4578–4588. 05B45 (91A46)
Review PDF Clipboard Journal Article 5 Citations
MR2379074 Reviewed Fraenkel, Aviezri S. Games played by Boole and
Galois. Discrete Appl. Math. 156 (2008), no. 4, 420–427. 91A46
Review PDF Clipboard Journal Article
MR2361163 Indexed Davis, Philip J.; Fraenkel, Aviezri S. Remembering Philip
Rabinowitz. Notices Amer. Math. Soc. 54 (2007), no. 11, 1502–1506. 01A70
Review PDF Clipboard Journal Article
MR2337048 Reviewed Fraenkel, Aviezri S.; Kontorovich, Alex The Sierpiński
sieve of Nim-varieties and binomial coefficients. Combinatorial number
theory, 209–227, de Gruyter, Berlin, 2007. (Reviewer: Kimmo Eriksson) 05A10
(11B65 91A46)
Review PDF Clipboard Series Chapter 5 Citations
MR2337047 Reviewed Fraenkel, Aviezri S. The Raleigh game. Combinatorial
number theory, 199–208, de Gruyter, Berlin, 2007. (Reviewer: E. J.
Barbeau) 91A46 (91A05)
Review PDF Clipboard Series Chapter 4 Citations
MR2184445 Reviewed Fraenkel, Aviezri S. Euclid and Wythoff games. Discrete
Math. 304 (2005), no. 1-3, 65–68. 91A05 (91A46)
Review PDF Clipboard Journal Article 12 Citations
MR2111926 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie An extension of the
periodicity lemma to longer periods. Discrete Appl. Math. 146 (2005), no.
2, 146–155. 68R15 (05A05)
Review PDF Clipboard Journal Article
MR2116012 Reviewed Fraenkel, Aviezri S. New games related to old and new
sequences. Integers 4 (2004), G6, 18 pp. (Reviewer: David Damanik) 11B83
(91A05)
Review PDF Clipboard Journal Article 10 Citations
MR2056945 Indexed Demaine, Erik D.; Fleischer, Rudolf; Fraenkel,
Aviezri; Nowakowski, Richard J. Appendix B: Open problems at the 2002
Dagstuhl Seminar on Algorithmic Combinatorial Game Theory. Algorithmic
combinatorial game theory. Theoret. Comput. Sci. 313 (2004), no.
3, 539–543. 91A46
Review PDF Clipboard Journal Article 2 Citations
MR2056935 Indexed Fraenkel, Aviezri S. Complexity, appeal and challenges of
combinatorial games. Algorithmic combinatorial game theory. Theoret. Comput.
Sci. 313 (2004), no. 3, 393–415. 91A46 (05A99 68Q25)
Review PDF Clipboard Journal Article 24 Citations
MR2056934 Reviewed Fekete, S�ndor P.; Fleischer, Rudolf; Fraenkel,
Aviezri; Schmitt, Matthias Traveling salesmen in the presence of
competition. Algorithmic combinatorial game theory. Theoret. Comput.
Sci. 313 (2004), no. 3, 377–392. 90C35 (68Q17 91A05)
Review PDF Clipboard Journal Article 6 Citations
MR2042724 Indexed Fraenkel, A. S. New games related to old and new
sequences. Advances in computer games (Graz, 2003), 367–382, IFIP Int. Fed.
Inf. Process., 135, Kluwer Acad. Publ., Boston, MA, 2004. 91A46
Review PDF Clipboard Series Chapter
MR2020683 Reviewed Fraenkel, Aviezri S.; Krieger, Dalia The structure of
complementary sets of integers: a 3-shift theorem. Int. J. Pure Appl.
Math. 10 (2004), no. 1, 1–49. (Reviewer: A. Ya. Olenko) 05A17 (05A05 91A05)
Review PDF Clipboard Journal Article 6 Citations
MR1973111 Indexed Fraenkel, Aviezri S. Combinatorial games: selected
bibliography with a succinct gourmet introduction. More games of no chance
(Berkeley, CA, 2000), 475–535, Math. Sci. Res. Inst. Publ., 42, Cambridge
Univ. Press, Cambridge, 2002. 91A46
Review PDF Clipboard Series Chapter 5 Citations
MR1973018 Reviewed Fraenkel, Aviezri S. Two-player games on cellular
automata. More games of no chance (Berkeley, CA, 2000), 279–306, Math. Sci.
Res. Inst. Publ., 42, Cambridge Univ. Press, Cambridge, 2002. 91A05 (05C85
68Q80 91A43 91A46)
Review PDF Clipboard Series Chapter 8 Citations
MR1954732 Reviewed Fraenkel, A. S.; Simpson, R. J.; Paterson, M. S. On
abelian circular squares in binary words. Paul Erdős and his mathematics, II
(Budapest, 1999), 329–338, Bolyai Soc. Math. Stud., 11, J�nos Bolyai Math.
Soc., Budapest, 2002. 68R15 (05A05)
Review PDF Clipboard Series Chapter
MR1909611 Indexed Fraenkel, Aviezri S. Virus versus mankind. Computers and
games (Hamamatsu, 2000), 204–213, Lecture Notes in Comput. Sci.,
2063, Springer, Berlin, 2002. 05C99 (68Q80 91A43)
Review PDF Clipboard Series Chapter 5 Citations
MR1909052 Reviewed Fraenkel, Aviezri S. Arrays, numeration systems and
Frankenstein games. FUN with algorithms (Elba, 1998). Theoret. Comput.
Sci. 282 (2002), no. 2, 271–284. (Reviewer: Prabir Das) 91A46 (11B37)
Review PDF Clipboard Journal Article 4 Citations
MR1904570 Indexed Fraenkel, Aviezri S.; Simpson, Jamie An extension of the
periodicity lemma to longer periods (invited lecture). Combinatorial pattern
matching (Jerusalem, 2001), 98–105, Lecture Notes in Comput. Sci.,
2089, Springer, Berlin, 2001. 68R15
Review PDF Clipboard Series Chapter 2 Citations
MR1853261 Reviewed Fraenkel, Aviezri S.; Seeman, Tamar; Simpson, Jamie The
subword complexity of a two-parameter family of sequences. In honor of
Aviezri Fraenkel on the occasion of his 70th birthday. Electron. J.
Combin. 8 (2001), no. 2, Research Paper 10, 19 pp. (Reviewer: Walter
Kern) 91A05 (68R15)
Review PDF Clipboard Journal Article 3 Citations
MR1806223 Reviewed Fraenkel, Aviezri S.; Rahat, Ofer Infinite cyclic
impartial games. Computer and games (Tsukuba, 1998). Theoret. Comput.
Sci. 252 (2001), no. 1-2, 13–22. 91A43 (05C20)
Review PDF Clipboard Journal Article 4 Citations
MR1806222 Reviewed Fraenkel, Aviezri S.; Zusman, Dmitri A new heap
game. Computer and games (Tsukuba, 1998). Theoret. Comput.
Sci. 252 (2001), no. 1-2, 5–12. 91A46 (68T20)
Review PDF Clipboard Journal Article 7 Citations
MR1798313 Reviewed Fraenkel, Aviezri S. Recent results and questions in
combinatorial game complexities. Combinatorial algorithms (Perth,
1998). Theoret. Comput. Sci. 249 (2000), no. 2, 265–288. (Reviewer: Daniel
Elliott Loeb) 91A46 (68Q25 68R05 91A40)
Review PDF Clipboard Journal Article 1 Citation
MR1781301 Reviewed Fraenkel, Aviezri S. On the recurrence fm+1=bmfm−fm−1 and
applications. Discrete Math. 224 (2000), no. 1-3, 273–279. (Reviewer: Vichian
Laohakosol) 39A10 (11A55 40A15)
Review PDF Clipboard Journal Article 1 Citation
MR1715689 Reviewed Fraenkel, Aviezri S.; Rahat, Ofer Infinite cyclic
impartial games. Computers and games (Tsukuba, 1998), 212–221, Lecture Notes
in Comput. Sci., 1558, Springer, Berlin, 1999. (Reviewer: P. A.
Biryukov) 91A46 (05C20)
Review PDF Clipboard Series Chapter 1 Citation
MR1715688 Reviewed Fraenkel, Aviezri S.; Zusman, Dmitri A new heap
game. Computers and games (Tsukuba, 1998), 205–211, Lecture Notes in Comput.
Sci., 1558, Springer, Berlin, 1999. (Reviewer: P. A. Biryukov) 91A46
Review PDF Clipboard Series Chapter 1 Citation
MR1688708 Reviewed Fraenkel, Aviezri S. Protein folding, spin glass and
computational complexity. DNA based computers III (Philadelphia, PA,
1997), 101–121, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 48, Amer.
Math. Soc., Providence, RI, 1999. (Reviewer: Stephen J. Willson) 92D20 (68Q25
92-08)
Review PDF Clipboard Series Chapter 5 Citations
MR1687768 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie The exact number of
squares in Fibonacci words. WORDS (Rouen, 1997). Theoret. Comput.
Sci. 218 (1999), no. 1, 95–106. (Reviewer: Patrice S��bold) 68R15 (11B39)
Review PDF Clipboard Journal Article 19 Citations
MR1543394 DML Fraenkel, Aviezri; Martin, Reiner; Problems and Solutions:
Solutions: Sets with Fixed Nim-Sum: 10564. Amer. Math.
Monthly 106 (1999), no. 1, 71–72.
Review PDF Clipboard Journal Article
MR1681514 Reviewed Fraenkel, Aviezri S. Heap games, numeration systems and
sequences. Ann. Comb. 2 (1998), no. 3, 197–210. 91A05 (05A99 91A46)
Review PDF Clipboard Journal Article 31 Citations
MR1656919 Reviewed Fraenkel, Aviezri S. Multivision: an intractable impartial
game with a linear winning strategy. Amer. Math. Monthly 105 (1998), no.
10, 923–928. (Reviewer: E. Marchi) 90D46 (05A99)
Review PDF Clipboard Journal Article 1 Citation
MR1652900 Reviewed Blass, Uri; Fraenkel, Aviezri S.; Guelman, Romina How far
can nim in diguise be stretched? J. Combin. Theory Ser. A 84 (1998), no.
2, 145–156. (Reviewer: P. A. Biryukov) 91A46 (05A99)
Review PDF Clipboard Journal Article 9 Citations
MR1638601 Reviewed Fraenkel, Aviezri S.; Ozery, Michal Adjoining to Wythoff's
game its P-positions as moves. Theoret. Comput. Sci. 205 (1998), no.
1-2, 283–296. (Reviewer: P. A. Biryukov) 90D46
Review PDF Clipboard Journal Article 16 Citations
MR1616571 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie How many squares can
a string contain? J. Combin. Theory Ser. A 82 (1998), no. 1, 112–120. 68R15
(11B85)
Review PDF Clipboard Journal Article 49 Citations
MR1608392 Reviewed Fraenkel, Aviezri S.; Simpson, Jamie; Paterson, Mike On
weak circular squares in binary words. Combinatorial pattern matching
(Aarhus, 1997), 76–82, Lecture Notes in Comput. Sci., 1264, Springer,
Berlin, 1997. 68R15
Review PDF Clipboard Series Chapter 3 Citations
MR1542936 DML Fraenkel, Aviezri; Bloom, D. M.; Suman, Kenneth; Myerson,
Gerry; Girod, Donald; Knuth, Donald E.; Priestley, W. M.; Deutsch,
Emeric; Problems and Solutions: Problems: 10564-10570. Amer. Math.
Monthly 104 (1997), no. 1, 68–69.
Review PDF Clipboard Journal Article
MR1444157 Reviewed Fraenkel, Aviezri S. Combinatorial game theory foundations
applied to digraph kernels. The Wilf Festschrift (Philadelphia, PA,
1996). Electron. J. Combin. 4 (1997), no. 2, Research Paper 10, approx. 17
pp. 05C90 (05C85 68Q25 90D43)
Review PDF Clipboard Journal Article 12 Citations
MR1427984 Indexed Fraenkel, Aviezri S. Combinatorial games: selected
bibliography with a succinct gourmet introduction. Games of no chance
(Berkeley, CA, 1994), 493–537, Math. Sci. Res. Inst. Publ., 29, Cambridge
Univ. Press, Cambridge, 1996. 90D46 (90-00)
Review PDF Clipboard Series Chapter 2 Citations
MR1427980 Reviewed Fraenkel, Aviezri S. Error-correcting codes derived from
combinatorial games. Games of no chance (Berkeley, CA, 1994), 417–431, Math.
Sci. Res. Inst. Publ., 29, Cambridge Univ. Press, Cambridge, 1996. (Reviewer:
Ram Autar) 94B05 (90D46)
Review PDF Clipboard Series Chapter 5 Citations
MR1427955 Reviewed Fraenkel, Aviezri S. Scenic trails ascending from
sea-level Nim to alpine chess. Games of no chance (Berkeley, CA,
1994), 13–42, Math. Sci. Res. Inst. Publ., 29, Cambridge Univ. Press,
Cambridge, 1996. (Reviewer: Imma J. Curiel) 90D46 (05C99 90D05)
Review PDF Clipboard Series Chapter 11 Citations
MR1364104 Reviewed Jones, J. P.; Fraenkel, A. S. Complexities of winning
strategies in Diophantine games. J. Complexity 11 (1995), no. 4, 435–455.
(Reviewer: John Michael Robson) 68Q25 (03D15 68Q15 90D46)
Review PDF Clipboard Journal Article 2 Citations
MR1336680 Reviewed Fraenkel, Aviezri S.; Loebl, Martin Complexity of circuit
intersection in graphs. Discrete Math. 141 (1995), no. 1-3, 135–151.
(Reviewer: Patrick Sol�) 05C85 (57M25)
Review PDF Clipboard Journal Article 1 Citation
MR1335685 Reviewed Fraenkel, Aviezri S.; Jaffray, Alan; Kotzig,
Anton; Sabidussi, Gert Modular Nim. Theoret. Comput. Sci. 143 (1995), no.
2, 319–333. (Reviewer: Edward W. Packel) 90D05 (00A08 05A99 90D42)
Review PDF Clipboard Journal Article 5 Citations
MR1310736 Reviewed Fraenkel, Aviezri S.; Holzman, Ron Gap problems for
integer part and fractional part sequences. J. Number Theory 50 (1995), no.
1, 66–86. (Reviewer: Robert F. Tichy) 11J71 (11K31)
Review PDF Clipboard Journal Article 16 Citations
MR1309124 Reviewed Fraenkel, Aviezri S.; Simpson, R. Jamie How many squares
must a binary sequence contain? Electron. J. Combin. 2 (1995), Research Paper
2, approx. 9 pp. (Reviewer: �kos Pint�r) 11B83 (05A99)
Review PDF Clipboard Journal Article 29 Citations
MR1670621 Indexed Fraenkel, Aviezri S. Combinatorial games: selected
bibliography with a succinct gourmet introduction. Electron. J.
Combin. 1 (1994), Dynamic Survey 2, 45 pp. 90-00 (05A99 90Dxx)
Review PDF Clipboard Journal Article 43 Citations
MR1310872 Reviewed Fraenkel, A. S.; Porta, H.; Stolarsky, K. B. The almost PV
behavior of some far from PV algebraic integers. Discrete
Math. 135 (1994), no. 1-3, 93–101. (Reviewer: D. Boyd) 11R06 (11B37 11J71)
Review PDF Clipboard Journal Article
MR1289489 Reviewed Fraenkel, A. S.; Klein, S. T. Complexity aspects of
guessing prefix codes. Algorithmica 12 (1994), no. 4-5, 409–419. (Reviewer:
Andrea Sgarro) 94A60 (68P25 68Q15 94A29 94A45)
Review PDF Clipboard Journal Article 2 Citations
MR1274978 Reviewed Bronstein, Victor; Fraenkel, Aviezri S. On a curious
property of counting sequences. Amer. Math. Monthly 101 (1994), no.
6, 560–563. (Reviewer: Giuseppe Pellegrino) 05A16
Review PDF Clipboard Journal Article 1 Citation
MR1269166 Reviewed Fraenkel, Aviezri Even kernels. Electron. J.
Combin. 1 (1994), Research Paper 5, approx. 13 pp. (Reviewer: Hans L.
Bodlaender) 05C70 (68Q25 68R10)
Review PDF Clipboard Journal Article
MR1264482 Reviewed Fraenkel, A. S.; Kimberling, Clark Generalized Wythoff
arrays, shuffles and interspersions. Discrete Math. 126 (1994), no.
1-3, 137–149. (Reviewer: Volker Strehl) 11B83 (05A99)
Review PDF Clipboard Journal Article 10 Citations
MR1138949 Reviewed Fraenkel, Aviezri S. Iterated floor function, algebraic
numbers, discrete chaos, Beatty subsequences, semigroups. Trans. Amer. Math.
Soc. 341 (1994), no. 2, 639–664. (Reviewer: Štefan Porubsk�) 11B83 (11B39
11Z50 58F13)
Review PDF Clipboard Journal Article 15 Citations
MR1216328 Reviewed Fraenkel, Aviezri S.; Scheinerman, Edward R.; Ullman,
Daniel Undirected edge geography. Theoret. Comput. Sci. 112 (1993), no.
2, 371–381. 90D35 (68Q25)
Review PDF Clipboard Journal Article 17 Citations
MR1210094 Reviewed Eggleton, Roger B.; Fraenkel, Aviezri S.; Simpson, R.
Jamie Beatty sequences and Langford sequences. Graph theory and combinatorics
(Marseille-Luminy, 1990). Discrete Math. 111 (1993), no. 1-3, 165–178.
(Reviewer: Š. Zn�m) 11B25 (05A10)
Review PDF Clipboard Journal Article 4 Citations
MR1208665 Reviewed Fraenkel, A. S.; Simonson, S. Geography. Theoret. Comput.
Sci. 110 (1993), no. 1, 197–214. 90D40 (05C85 68Q25 68R10 90D35)
Review PDF Clipboard Journal Article 11 Citations
MR1148023 Reviewed Fraenkel, Aviezri S.; Simpson, R. Jamie On infinite
disjoint covering systems. Proc. Amer. Math. Soc. 119 (1993), no. 1, 5–9.
(Reviewer: Š. Zn�m) 11B25
Review PDF Clipboard Journal Article 2 Citations
MR1214102 Reviewed Barabash, Alexander; Fraenkel, Aviezri S.; Weiss,
Barak Iterated Beatty functions. Random Comput. Dynam. 1 (1992/93), no.
3, 333–348. (Reviewer: R. G. Stoneham) 11B34 (11B75)
Review PDF Clipboard Journal Article 1 Citation
MR1130685 Reviewed Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.; Holzman,
R. On infinite and finite covering systems. Amer. Math.
Monthly 98 (1991), no. 8, 739–742. (Reviewer: Anne Ludington Young) 11B05
(11B50)
Review PDF Clipboard Journal Article 2 Citations
MR1119698 Reviewed Fraenkel, Aviezri S.; Lorberbom, Mordechai Nimhoff
games. J. Combin. Theory Ser. A 58 (1991), no. 1, 1–25. (Reviewer: Daniel
Elliott Loeb) 90D46 (68Q25)
Review PDF Clipboard Journal Article 24 Citations
MR1095546 Indexed Fraenkel, Aviezri S. Selected bibliography on combinatorial
games and some related material. Combinatorial games (Columbus, OH,
1990), 191–226, Proc. Sympos. Appl. Math., 43, AMS Short Course Lecture
Notes, Amer. Math. Soc., Providence, RI, 1991. 90D46 (05A99)
Review PDF Clipboard Series Chapter
MR1095543 Indexed Fraenkel, Aviezri S. Complexity of games. Combinatorial
games (Columbus, OH, 1990), 111–153, Proc. Sympos. Appl. Math., 43, AMS Short
Course Lecture Notes, Amer. Math. Soc., Providence, RI, 1991. 90D46 (05A99)
Review PDF Clipboard Series Chapter 2 Citations
MR1095370 Reviewed Fraenkel, Aviezri S.; Scheinerman, Edward R. A deletion
game on hypergraphs. ARIDAM III (New Brunswick, NJ, 1988). Discrete Appl.
Math. 30 (1991), no. 2-3, 155–162. 90D43 (05C65)
Review PDF Clipboard Journal Article 9 Citations
MR1084184 Reviewed Fraenkel, A. S.; Porta, H.; Stolarsky, K. B. Some
arithmetical semigroups. Analytic number theory (Allerton Park, IL,
1989), 255–264, Progr. Math., 85, Birkh�user Boston, Boston, MA, 1990.
(Reviewer: F. Beukers) 11A05 (20M14)
Review PDF Clipboard Series Chapter 5 Citations
MR1081578 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Irreducible disjoint covering systems (with an application to Boolean
algebra). First International Colloquium on Pseudo-Boolean Optimization and
Related Topics (Chexbres, 1987). Discrete Appl. Math. 29 (1990), no.
2-3, 143–164. (Reviewer: Ivan Korec) 20D60 (03B05 03G05 11B25)
Review PDF Clipboard Journal Article
MR1080539 Reviewed Blass, Uri; Fraenkel, Aviezri S. The Sprague-Grundy
function for Wythoff's game. Theoret. Comput. Sci. 75 (1990), no. 3, 311–333.
(Reviewer: Jos Potters) 90D43
Review PDF Clipboard Journal Article 19 Citations
MR1075260 Reviewed Fraenkel, A. S.; Klein, S. T. Bidirectional Huffman
coding. Comput. J. 33 (1990), no. 4, 296–307. (Reviewer: Alexander
Barg) 94A29
Review PDF Clipboard Journal Article 7 Citations
MR1031263 Reviewed Fraenkel, Aviezri S.; Lorberbom, Mordechai Epidemiography
with various growth functions. Combinatorics and complexity (Chicago, IL,
1987). Discrete Appl. Math. 25 (1989), no. 1-2, 53–71. (Reviewer: A.
Pultr) 90D05 (90D42 92A20)
Review PDF Clipboard Journal Article 3 Citations
MR1024962 Reviewed Fraenkel, A. S.; Harary, F. Geodetic contraction games on
graphs. Internat. J. Game Theory 18 (1989), no. 3, 327–338. (Reviewer: Prabir
Das) 90D05 (05C99)
Review PDF Clipboard Journal Article 2 Citations
MR1009869 Reviewed Duvdevani, N.; Fraenkel, A. S. Properties of k-Welter's
game. Discrete Math. 76 (1989), no. 3, 197–221. (Reviewer: Victor J.
Baston) 90D05 (05A99 90D42)
Review PDF Clipboard Journal Article 3 Citations
MR0992303 Reviewed Fraenkel, Aviezri S. The use and usefulness of numeration
systems. Inform. and Comput. 81 (1989), no. 1, 46–61. 68Q20 (20F99)
Review PDF Clipboard Journal Article
MR0983032 Reviewed Agur, Z.; Fraenkel, A. S.; Klein, S. T. Errata to: "The
number of fixed points of the majority rule''. Discrete Math. 73 (1989), no.
3, 321. (Reviewer: K. B. Reid) 05A15 (68Q80 90A08 92A10 92A20)
Review PDF Clipboard Journal Article 1 Citation
MR0991211 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Mycielski-Sierpiński conjecture and Korec-Zn�m result. Colloq.
Math. 56 (1988), no. 2, 241–249. (Reviewer: Michael E. Mays) 20D60 (11A07
20D50)
Review PDF Clipboard Journal Article 2 Citations
MR0957212 Reviewed Fraenkel, Aviezri S.; Loebl, Martin; Nes̆etr̆il,
Jaroslav Epidemiography. II. Games with a dozing yet winning player. J.
Combin. Theory Ser. A 49 (1988), no. 1, 129–144. 90D42 (05C20 90D05)
Review PDF Clipboard Journal Article 4 Citations
MR0955126 Reviewed Agur, Z.; Fraenkel, A. S.; Klein, S. T. The number of
fixed points of the majority rule. Discrete Math. 70 (1988), no. 3, 295–302.
(Reviewer: K. B. Reid) 05A15 (68Q80 90A08 92A10 92A20)
Review PDF Clipboard Journal Article 16 Citations
MR0945272 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Improvements to the Newman-Zn�m result for disjoint covering systems. Acta
Arith. 50 (1988), no. 1, 1–13. (Reviewer: Š. Zn�m) 11A07 (11B25)
Review PDF Clipboard Journal Article 4 Citations
MR0945267 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Disjoint covering systems with precisely one multiple modulus. Acta
Arith. 50 (1988), no. 2, 171–182. (Reviewer: Š. Zn�m) 11B25 (11A07)
Review PDF Clipboard Journal Article 1 Citation
MR0942479 Reviewed Berger, Marc A.; Erdős, Paul; Felzenbaum,
Alexander; Fraenkel, Aviezri S. Nearly disjoint covering systems. Eleventh
British Combinatorial Conference (London, 1987). Ars
Combin. 25 (1988), B, 231–246. (Reviewer: R. C. Mullin) 11A07
Review PDF Clipboard Journal Article
MR0939862 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Covers of product sets and the Korec-Zn�m result. European J.
Combin. 9 (1988), no. 2, 131–138. (Reviewer: Ivan Korec) 11B25
Review PDF Clipboard Journal Article
MR0922566 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel,
Aviezri Remark on the multiplicity of a partition of a group into
cosets. Fund. Math. 128 (1987), no. 3, 139–144. (Reviewer: F. P�rez
Monasor) 20D60 (20D20)
Review PDF Clipboard Journal Article 5 Citations
MR0899900 Reviewed Fraenkel, Aviezri S.; Goldschmidt,
Elisheva PSPACE-hardness of some combinatorial games. J. Combin. Theory Ser.
A 46 (1987), no. 1, 21–38. (Reviewer: Andreas Blass) 68Q15 (05C20 90D05
90D42)
Review PDF Clipboard Journal Article 7 Citations
MR0899899 Reviewed Kahane, Joseph; Fraenkel, Aviezri S. k-Welter—a
generalization of Welter's game. J. Combin. Theory Ser. A 46 (1987), no.
1, 1–20. (Reviewer: Victor J. Baston) 90D05 (05A99 90D42)
Review PDF Clipboard Journal Article 5 Citations
MR0893463 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Necessary condition for the existence of an incongruent covering system
with odd moduli. II. Acta Arith. 48 (1987), no. 1, 73–79. (Reviewer: Š.
Zn�m) 11A07
Review PDF Clipboard Journal Article 2 Citations
MR0891542 Reviewed Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S. Lattice
parallelotopes and disjoint covering systems. Discrete Math. 65 (1987), no.
1, 23–46. (Reviewer: Š. Zn�m) 11B25 (11A07)
Review PDF Clipboard Journal Article 4 Citations
MR0887178 Reviewed Fraenkel, A. S.; Kotzig, A. Partizan octal games: partizan
subtraction games. Internat. J. Game Theory 16 (1987), no. 2, 145–154.
(Reviewer: G. A. Heuer) 90D05
Review PDF Clipboard Journal Article 9 Citations
MR0880165 Reviewed Apostolico, Alberto; Fraenkel, Aviezri S. Robust
transmission of unbounded strings using Fibonacci representations. IEEE
Trans. Inform. Theory 33 (1987), no. 2, 238–245. (Reviewer: Andrea
Sgarro) 94B45 (94A29)
Review PDF Clipboard Journal Article 15 Citations
MR0875291 Reviewed Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S. A
nonanalytic proof of the Newman-Zn�m result for disjoint covering
systems. Combinatorica 6 (1986), no. 3, 235–243. (Reviewer: Š. Zn�m) 11B25
(11A07 11B83)
Review PDF Clipboard Journal Article 10 Citations
MR0867643 Reviewed Fraenkel, Aviezri S.; Yesha, Yaacov The generalized
Sprague-Grundy function and its invariance under certain mappings. J. Combin.
Theory Ser. A 43 (1986), no. 2, 165–177. (Reviewer: Harold Reiter) 90D42
(05C20)
Review PDF Clipboard Journal Article 8 Citations
MR0847297 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel,
Aviezri Necessary condition for the existence of an incongruent covering
system with odd moduli. Acta Arith. 45 (1986), no. 4, 375–379. (Reviewer: Š.
Zn�m) 11A07
Review PDF Clipboard Journal Article 1 Citation
MR0846712 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel,
Aviezri The Herzog-Sch�nheim conjecture for finite nilpotent groups. Canad.
Math. Bull. 29 (1986), no. 3, 329–333. (Reviewer: E. I. Khukhro) 20D60
(20D15)
Review PDF Clipboard Journal Article 6 Citations
MR0843471 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Disjoint covering systems of rational Beatty sequences. J. Combin. Theory
Ser. A 42 (1986), no. 1, 150–153. (Reviewer: Calvin T. Long) 11B75 (11B83)
Review PDF Clipboard Journal Article 5 Citations
MR0818066 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. New results for covering systems of residue sets. Bull. Amer. Math. Soc.
(N.S.) 14 (1986), no. 1, 121–126. (Reviewer: Štefan Porubsk�) 11B25
Review PDF Clipboard Journal Article 4 Citations
MR0824850 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Improvements to two results concerning systems of residue sets. Ars
Combin. 20 (1985), 69–82. (Reviewer: Š. Zn�m) 11A07
Review PDF Clipboard Journal Article 4 Citations
MR0815340 Reviewed Fraenkel, Aviezri S. The use and usefulness of numeration
systems. Combinatorial algorithms on words (Maratea, 1984), 187–203, NATO
Adv. Sci. Inst. Ser. F: Comput. Systems Sci., 12, Springer, Berlin, 1985.
(Reviewer: D. A. Klarner) 68Q20 (68P05 68R05)
Review PDF Clipboard Series Chapter
MR0815339 Indexed Fraenkel, Aviezri S.; Klein, Shmuel T. Novel compression of
sparse bit-strings—preliminary report. Combinatorial algorithms on words
(Maratea, 1984), 169–183, NATO Adv. Sci. Inst. Ser. F: Comput. Systems Sci.,
12, Springer, Berlin, 1985. 68P99
Review PDF Clipboard Series Chapter 3 Citations
MR0789177 Reviewed Fraenkel, Aviezri S.; Nes̆etr̆il,
Jaroslav Epidemiography. Pacific J. Math. 118 (1985), no. 2, 369–381.
(Reviewer: Klaus Lommatzsch) 90D05 (05C20)
Review PDF Clipboard Journal Article 3 Citations
MR0777556 Reviewed Fraenkel, Aviezri S. Systems of numeration. Amer. Math.
Monthly 92 (1985), no. 2, 105–114. (Reviewer: Torleiv Kl�ve) 11B37
Review PDF Clipboard Journal Article 103 Citations
Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S. Irreducible
disjoint covering systems (with an application to Boolean algebra). First
International Colloquium on Pseudo-Boolean Optimization and Related Topics
(Chexbres, 1987). Discrete Appl. Math. 29 (1990), no. 2-3, 143–164.
Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Mycielski-Sierpiński conjecture and Korec-Zn�m result. Colloq.
Math. 56 (1988), no. 2, 241–249.
MR0945272 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Improvements to the Newman-Zn�m result for disjoint covering systems. Acta
Arith. 50 (1988), no. 1, 1–13. (Reviewer: Š. Zn�m) 11A07 (11B25)
Review PDF Clipboard Journal Article 4 Citations
MR0945267 Reviewed Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri
S. Disjoint covering systems with precisely one multiple modulus. Acta
Arith. 50 (1988), no. 2, 171–182. (Reviewer: Š. Zn�m) 11B25 (11A07)
Review PDF Clipboard Journal Article 1 Citation
MR0791023 Reviewed Fraenkel, Aviezri S.; Hammer, Peter L. Pseudo-Boolean
functions and their graphs. Convexity and graph theory (Jerusalem,
1981), 137–146, North-Holland Math. Stud., 87, Ann. Discrete Math.,
20, North-Holland, Amsterdam, 1984. (Reviewer: Pavol Hell) 90C99 (05C99
06E30)
Review PDF Clipboard Series Chapter 3 Citations
MR0744489 Reviewed Boshernitzan, M.; Fraenkel, A. S. A linear algorithm for
nonhomogeneous spectra of numbers. J. Algorithms 5 (1984), no. 2, 187–198.
(Reviewer: Richard T. Bumby) 11Y55 (68Q40)
Review PDF Clipboard Journal Article 9 Citations
MR0742402 Reviewed Fraenkel, Aviezri S. Wythoff games, continued fractions,
cedar trees and Fibonacci searches. Theoret. Comput. Sci. 29 (1984), no.
1-2, 49–73. 68Q20 (05A99 90D05)
Review PDF Clipboard Journal Article 25 Citations
MR0732206 Reviewed Mor, M.; Fraenkel, A. S. Cayley permutations. Discrete
Math. 48 (1984), no. 1, 101–112. (Reviewer: M. Livingston) 05A15 (05A05
05C05)
Review PDF Clipboard Journal Article 7 Citations
MR0741904 Reviewed Fraenkel, Aviezri S.; Mor, Moshe Combinatorial compression
and partitioning of large dictionaries. Comput. J. 26 (1983), no.
4, 336–343. 68P99 (68R05)
Review PDF Clipboard Journal Article
MR0732312 Reviewed Fraenkel, A. S.; Mor, M.; Perl, Y. Is text compression by
prefixes and suffixes practical? Acta Inform. 20 (1983), no.
4, 371–389. 68U15 (94A29)
Review PDF Clipboard Journal Article
MR0727659 Reviewed Fraenkel, Aviezri S. Wythoff games, continued fractions,
cedar trees and Fibonacci searches. Automata, languages and programming
(Barcelona, 1983), 203–225, Lecture Notes in Comput. Sci., 154, Springer,
Berlin, 1983. 68Q20 (11B39 90D05)
Review PDF Clipboard Series Chapter
MR0691047 Reviewed Mor, M.; Fraenkel, A. S. Permutation generation on vector
processors. Comput. J. 25 (1982), no. 4, 423–428. 68E99 (05A05 68C05)
Review PDF Clipboard Journal Article
MR0678172 Reviewed Fraenkel, A. S.; Yesha, Y. Theory of annihilation games.
I. J. Combin. Theory Ser. B 33 (1982), no. 1, 60–86. (Reviewer: Selim G.
Akl) 90D05 (05C20)
Review PDF Clipboard Journal Article 6 Citations
MR0675171 Reviewed Fraenkel, L. E. On the embedding of C1(Ω�) in C0,α(Ω�). J.
London Math. Soc. (2) 26 (1982), no. 2, 290–298. (Reviewer: J. S.
Martins) 46E35
Review PDF Clipboard Journal Article
MR0671176 Reviewed Fraenkel, Aviezri S.; Tassa, Uzi Strategies for compounds
of partizan games. Math. Proc. Cambridge Philos. Soc. 92 (1982), no.
2, 193–204. 90D05
Review PDF Clipboard Journal Article 3 Citations
MR0666110 Reviewed Amick, C. J.; Fraenkel, L. E.; Toland, J. F. On the Stokes
conjecture for the wave of extreme form. Acta Math. 148 (1982), 193–214.
(Reviewer: Alberto Valli) 35R35 (76B15)
Review PDF Clipboard Journal Article 116 Citations
MR0660914 Reviewed Fraenkel, Aviezri S. How to beat your Wythoff games'
opponent on three fronts. Amer. Math. Monthly 89 (1982), no.
6, 353–361. 90D05
Review PDF Clipboard Journal Article 56 Citations
MR0675689 Reviewed Fraenkel, Aviezri S. Planar kernel and Grundy
with d≤3, dout≤2, din≤2 are NP-complete. Discrete Appl. Math. 3 (1981), no.
4, 257–262. 68C25 (05C20)
Review PDF Clipboard Journal Article 29 Citations
MR0635143 Reviewed Fraenkel, Aviezri S.; Lichtenstein, David Computing a
perfect strategy for n�n chess requires time exponential in N. Automata,
languages and programming (Akko, 1981), pp. 278–293, Lecture Notes in Comput.
Sci., 115, Springer, Berlin-New York, 1981. 90D05 (68C25)
Review PDF Clipboard Series Chapter 5 Citations
MR0629595 Reviewed Fraenkel, Aviezri S.; Lichtenstein, David Computing a
perfect strategy for n�n chess requires time exponential in n. J. Combin.
Theory Ser. A 31 (1981), no. 2, 199–214. 68C25 (90D05)
Review PDF Clipboard Journal Article 11 Citations
MR0616779 Reviewed Fraenkel, L. E. A lower bound for electrostatic capacity
in the plane. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), no.
3-4, 267–273. 78A30 (31A15 49G05 52A40)
Review PDF Clipboard Journal Article 5 Citations
MR0613413 Reviewed Boshernitzan, M.; Fraenkel, A. S. Nonhomogeneous spectra
of numbers. Discrete Math. 34 (1981), no. 3, 325–327. 10L10
Review PDF Clipboard Journal Article 11 Citations
MR1572333 DML Fraenkel, Aviezri S.; Herda, Hans; News and Letters. Math.
Mag. 53 (1980), no. 1, 59–61.
Review PDF Clipboard Journal Article
MR0593528 Reviewed Fraenkel, Aviezri S. From Nim to Go. Ann. Discrete
Math. 6 (1980), 137–156. (Reviewer: Harold Reiter) 90D05 (05C20 68C25)
Review PDF Clipboard Journal Article 1 Citation
MR1567093 DML Fraenkel, Aviezri S.; Book Review: On numbers and games // Book
Review: Surreal numbers. Bull. Amer. Math. Soc. 84 (1978), no. 6, 1328–1336.
Review PDF Clipboard Journal Article
MR0523586 Reviewed Fraenkel, A. S.; Mushkin, M.; Tassa, U. Determination
of [nθ] by its sequence of differences. Canad. Math. Bull. 21 (1978), no.
4, 441–446. (Reviewer: Maurice Mignotte) 10F20 (10A30)
Review PDF Clipboard Journal Article 18 Citations
MR0496795 Reviewed Fraenkel, Aviezri S.; Tassa, Uzi; Yesha, Yaacov Three
annihilation games. Math. Mag. 51 (1978), no. 1, 13–17. (Reviewer: Stanisław
Zdrzałka) 90D99
Review PDF Clipboard Journal Article 1 Citation
MR0464779 Reviewed Attar, R.; Choueka, Y.; Dershowitz, N.; Fraenkel, A.
S. KEDMA—linguistic tools for retrieval systems. J. Assoc. Comput.
Mach. 25 (1978), no. 1, 52–66. (Reviewer: K. H. V. Booth) 68A50
Review PDF Clipboard Journal Article
MR0429815 Reviewed Fraenkel, Aviezri S. Complementary systems of
integers. Amer. Math. Monthly 84 (1977), no. 2, 114–115. (Reviewer:
Jau-Shyong Shiue) 10L05 (10A40)
Review PDF Clipboard Journal Article 8 Citations
MR0449726 Reviewed Fraenkel, A. S.; Yesha, Y. Theory of annihilation
games. Bull. Amer. Math. Soc. 82 (1976), no. 5, 775–777. (Reviewer: Richard
K. Guy) 90D05 (05C20)
Review PDF Clipboard Journal Article 4 Citations
MR0414115 Reviewed Fraenkel, A. S.; Tassa, U. Strategy for a class of games
with dynamic ties. Comput. Math. Appl. 1 (1975), no. 2, 237–254. (Reviewer:
Richard K. Guy) 90D05
Review PDF Clipboard Journal Article 4 Citations
MR0384171 Reviewed Fraenkel, A. S.; Perl, Y. Constructions in combinatorial
games with cycles. Infinite and finite sets (Colloq., Keszthely, 1973;
dedicated to P. Erdős on his 60th birthday), Vols. I, II, III, pp. 667–699.
Colloq. Math. Soc. J�nos Bolyai, Vol. 10, North-Holland, Amsterdam, 1975.
(Reviewer: R. K. Guy) 90D05 (05C20)
Review PDF Clipboard Series Chapter 5 Citations
MR0376591 Reviewed Borosh, I.; Fraenkel, A. S. A generalization of Jarn�k's
theorem on Diophantine approximations to Ridout type numbers. Trans. Amer.
Math. Soc. 211 (1975), 23–38. (Reviewer: Roland Fischer) 10K15
Review PDF Clipboard Journal Article
MR0374076 Reviewed Fraenkel, Aviezri S. Further characterizations and
properties of exactly covering congruences. Discrete Math. 12 (1975), 93–100;
erratum, ibid. 12 (1975), no. 4, 397. (Reviewer: A. J. Zajta) 10L05
Review PDF Clipboard Journal Article 1 Citation
MR0354027 Reviewed Fraenkel, Aviezri S. Combinatorial games with an
annihilation rule. The influence of computing on mathematical research and
education (Proc. Sympos. Appl. Math., Vol. 20, Univ. Montana, Missoula,
Mont., 1973), pp. 87–91. Amer. Math. Soc., Providence, R.I., 1974. (Reviewer:
T. L. Saaty) 90D05
Review PDF Clipboard Series Chapter 3 Citations
MR0339824 Reviewed Fraenkel, A. S.; Borosh, I. A generalization of Wythoff's
game. J. Combinatorial Theory Ser. A 15 (1973), 175–191. (Reviewer: Richard
K. Guy) 90D05
Review PDF Clipboard Journal Article 14 Citations
MR0316359 Reviewed Fraenkel, Aviezri S. A characterization of exactly
covering congruences. Discrete Math. 4 (1973), 359–366. (Reviewer: J. M.
Gandhi) 10A10 (10A35)
Review PDF Clipboard Journal Article 6 Citations
MR0309770 Reviewed Fraenkel, Aviezri S. Complementing and exactly covering
sequences. J. Combinatorial Theory Ser. A 14 (1973), 8–20. (Reviewer: A.
Zajta) 05B40
Review PDF Clipboard Journal Article 30 Citations
MR0308060 Reviewed Borosh, I.; Fraenkel, A. S. A generalization of Jarn�k's
theorem on Diophantine approximations. Nederl. Akad. Wetensch. Proc. Ser.
A 75=Indag. Math. 34 (1972), 193–201. (Reviewer: W. W. Adams) 10F10
Review PDF Clipboard Journal Article 17 Citations
MR0302599 Reviewed Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni,
Michael Characterization of the set of values f(n)=[nα], n=1,2,⋯. Discrete
Math. 2 (1972), no. 4, 335–345. (Reviewer: R. E. Greenwood) 10L10
Review PDF Clipboard Journal Article 10 Citations
MR0321866 Reviewed Fraenkel, Aviezri S. Diophantine equations involving
generalized triangular and tetrahedral numbers. Computers in number theory
(Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969), pp.
99–114. Academic Press, London, 1971. (Reviewer: J. Riordan) 10A40 (10B35)
Review PDF Clipboard Series Chapter
MR0294157 Reviewed Fraenkel, A. S. "Economic traversal of labyrinths'':
Correction. Math. Mag. 44 (1971), 12. 05C35
Review PDF Clipboard Journal Article
MR0265194 Reviewed Fraenkel, A. S. Economic traversal of labyrinths. Math.
Mag. 43 (1970), 125–130. 05.40
Review PDF Clipboard Journal Article 2 Citations
MR0234900 Reviewed Fraenkel, Aviezri S. The bracket function and
complementary sets of integers. Canadian J. Math. 21 (1969), 6–27. (Reviewer:
B. Garrison) 10.05
Review PDF Clipboard Journal Article 32 Citations
MR0188159 Reviewed Fraenkel, A. S.; Borosh, I. Corrigendum: Fractional
dimension of a set of transcendental numbers. Proc. London Math. Soc.
(3) 16 (1966), 192. 10.32
Review PDF Clipboard Journal Article
MR0187379 Reviewed Borosh, I.; Fraenkel, A. S. Exact solutions of linear
equations with rational coefficients by congruence techniques. Math.
Comp. 20 (1966), 107–112. (Reviewer: B. N. Parlett) 65.35
Review PDF Clipboard Journal Article 6 Citations
MR0177949 Reviewed Fraenkel, A. S.; Borosh, I. Fractional dimension of a set
of transcendental numbers. Proc. London Math. Soc. (3) 15 (1965), 458–470.
(Reviewer: J. Popken) 10.32
Review PDF Clipboard Journal Article 1 Citation
MR0170860 Reviewed Fraenkel, Aviezri S. Distance to the nearest integer and
algebraic independence of certain real numbers. Proc. Amer. Math.
Soc. 16 (1965), 154–160. (Reviewer: W. J. LeVeque) 10.32
Review PDF Clipboard Journal Article
MR0164932 Reviewed Fraenkel, Aviezri S. Transcendental numbers and a
conjecture of Erdős and Mahler. J. London Math. Soc. 39 (1964), 405–416.
(Reviewer: G. J. Rieger) 10.32
Review PDF Clipboard Journal Article 2 Citations
MR0154841 Reviewed Fraenkel, Aviezri S. New proof of the generalized Chinese
Remainder Theorem. Proc. Amer. Math. Soc. 14 (1963), 790–791. (Reviewer: D.
H. Lehmer) 10.06 (10.09)
Review PDF Clipboard Journal Article 1 Citation
MR0153613 Reviewed Gordon, B.; Fraenkel, A. S.; Straus, E. G. On the
determination of sets by the sets of sums of a certain order. Pacific J.
Math. 12 (1962), 187–196. (Reviewer: L. Moser) 10.62 (10.05)
Review PDF Clipboard Journal Article 4 Citations
MR0146990 Reviewed Cantor, D. G.; Estrin, G.; Fraenkel, A. S.; Turn, R. A
very high-speed digital number sieve. Math. Comp. 16 (1962), 141–154.
(Reviewer: D. H. Lehmer) 68.00 (10.64)
Review PDF Clipboard Journal Article 2 Citations
MR0144852 Reviewed Fraenkel, Aviezri S. On a theorem of D. Ridout in the
theory of Diophantine approximations. Trans. Amer. Math.
Soc. 105 (1962), 84–101. (Reviewer: J. Popken) 10.30
Review PDF Clipboard Journal Article 4 Citations
MR2939204 Thesis Fraenkel, Aviezri S. RATIONAL APPROXIMATIONS TO ALGEBRAIC
NUMBERS. Thesis (Ph.D.)–University of California, Los Angeles. 1961. (no
paging), ProQuest LLC
Review PDF Clipboard Series Thesis
MR0122019 Reviewed Fraenkel, Aviezri S. The use of index calculus and
Mersenne primes for the design of a high-speed digital multiplier. J. Assoc.
Comput. Mach. 8 (1961), 87–96. (Reviewer: C. B. Haselgrove) 68.00
Review PDF Clipboard Journal Article 1 Citation
A.S. Fraenkel,
Wythoff Games, Continued Fractions, Cedar Trees and Fibonacci Searches
Theoretical Computer Science (1984) 49-73
A.S. Fraenkel and I. Borosh, A generalization of Wythoff's game, J. Combin.
Theory , (1973) 175--191.
III. Hebrew Transliterated Reprints
* A.S. Fraenkel, Eileh v'eileh, in Hebrew. 'Hama'ayan, July 2023.
* A.S. Fraenkel, Midat ha'anava' at alit al kulana , in Hebrew; 'Hama'ayan,
December 2022.
* A.S. Fraenkel, T'guva Litguva Transliteration , in Hebrew; appeared in
'Hama'ayan, July 2022.
* A.S. Fraenkel, Yachasey gomlin beyn Beth Din l'veyn mitdaynim, (in
Hebrew). Appeared in "Hama'ayan", Chanuka, Tashpav, December 2021.
* A.S. Fraenkel, Al hilchot hashacheyn hachiloni (in Hebrew). Hatzofe Erev
shabbat Mas'ey, ha-tashsach, Aug. 1, 2008, p. 40.
* A.S. Fraenkel, Sifrei Chayim v'sifrei Meitim P'tuchim lfanav (in Hebrew).
Hama'ayan 48, Issue 1, Tishrei ha-tashsach, September 2007, pp. 34--37,
* A.S. Fraenkel, Hirhurim m'atim al proyekt hashu''t (in Hebrew) {\it
Hatzofe\/} Erev Shabbat Hagadol, 11 Nissan ha-tashsaz, March 30, 2007, pp.
11,14.
* A.S. Fraenkel, Madua ein korin korban musaf shel shabbat b'shabbat -- B,
in Hebrew. Hama'ayan 47, Issue 3, Nissan Ha-Tashsaz, March 2007, pp.
25--29.
* A.S. Fraenkel, Al t'filot ha'amida shel arvit, shacharit, mincha umisfei
rosh chodesh, in Hebrew. Moriya 27, Issue 9-10, pp. 85--89, Tevet
Ha-tashsav, Jan 2006.
* A.S. Fraenkel, Korban pesach b'veit hamikdash: She'elat z'man umakom, in
Hebrew. Sefer hazikaron ``Yoseif Da'at" l'zichro shel Yoseif Aharon Nitzan
za"l (Memorial volume commemorating the memory of the late Yosef Aharon
Nitzan), Sh'vat Ha-tashsav (Feb 2006), pp. 238--244.
* A.S. Fraenkel, Vaykonein Yirm'yahu al Yoshiyahu, in Hebrew. Hatzofe Erev
Shabbat Pinchas, ha-tashsad, July 9, 2004, p. 14.
* A.S. Fraenkel, Mikra'ot b'chag hashavu'ot v'darchei heyseik (in Hebrew).
Dedicated to the memory of Prof. Shalom (Freddy) Hirshfeld, za''l, Hatzofe
Erev Chag Hashavuot, ha-tashsad, May 25, 2004, p. 13.
* A.S. Fraenkel, Meshech Chochma l'sar haTorah, in Hebrew. Dedicated to the
memory of Dr. Zvi Betzer, za"l, Hatzofe Erev Shabbat Ki Tavo, ha-tashsag,
Sept 12, 2003, p. 12, 14
* A.S. Fraenkel, Sukkot B'Shavu'ot, in Hebrew. Hatzofe Erev Shabbat
Sh'lach-L'cha, ha-tashsag, June 20, 2003, p. 14
* A.S. Fraenkel, hitmachut, mumchiyut utchumim, in Hebrew. Hatzofe Erev
Shabbat Vayeishev, erev chag haChanukah, ha-tashsag, Nov 29, 2002, p. 11.
* S. Yedid and A.S. Fraenkel, Hashofeit kol ha'aretz lo ya'aseh mishpat?, in
Hebrew. Dedicated to the memory of Dr. Zvi Betzer, za"l, Hatzofe Erev
Shabbat Vayeira, ha-tashsag, Oct 25, 2002, p. 14.
* A.S. Fraenkel, R'galim, korbanot, avodah zarah, in Hebrew. Hatzofe Erev
chag haSukkot, ha-tashsag, Sept 20, 2002, p. 13.
* A.S. Fraenkel, Bein yachid l'tzibbur biymei din, in Hebrew. Hatzofe 1st
part: Erev Rosh Hashanah, ha-tashsag, Sept 6, 2002, pp. 12--13; 2nd part:
Erev Yom Kippur, Sept 15, 2002, p. 4.
* A.S. Fraenkel, He'arot z'irot (2), in Hebrew. Hatzofe (under the title
"Zeicheir liy'tzi'at mitzrayim") Erev Shabbat Hagadol, 13 Nissan,
ha-tashsa; April 4, 2001, pp. 12-13.
* A.S. Fraenkel He'arot z'irot (1), in Hebrew. Hatzofe Erev Shabbat
Mishpatim, parashat Sh'kalim, 1 Adar, ha-tashsa; Feb 23, 2001, pp. 14-15.
* A.S. Fraenkel M'sirut nefesh ugvurat nefesh, in Hebrew. Hatzofe Erev
Shabbat Bo, 9 Sh'vat, ha-tashsa; Feb 2, 2001, p. 10.
* A.S. Fraenkel Al ``Meshech Chochma'', in Hebrew. Hatzofe (under the title
'Bein n'vuat emet linvuat sheker (al echad meiekronot haparshanut shel
ha"meshech chochmah")', Erev Shabbat Tol'dot, 4 Kisleiv ha-tashsa; Dec 1,
2000, p. 8.
* A.S. Fraenkel, Bein yehudim lishe'einam yehudim, in Hebrew. Hatzofe,
Appeared in two parts: Erev Shavuot, 5 Sivan ha-tashas, June 8, 2000; and
Erev Shabbat B'ha'alotcha, 13 Sivan ha-tashas; June 16, 2000.
* A.S. Fraenkel, Simaniyot baMikra, in Hebrew. Hatzofe, Erev Shabbat
K'doshim, 30 Nissan ha-tashas; May 5, 2000.
* A.S. Fraenkel, Hadramah hashnatit, in Hebrew. Hatzofe, Erev Shabbat
Vayigash, 8 Teiveit ha-tashas; Dec. 17, 1999, p. 12.
* A.S. Fraenkel, T'filah: keifel teivot umiktzat hanhagot shel shatz, in
Hebrew. Hatzofe, Erev Rosh Hashanah ha-tashas, 29 Elul ha-tashnat; Sept.
10, 1999, pp. 16--17.
* A.S. Fraenkel, Chidon otzrot yisraeil, in Hebrew. In Memorial Volume
commemorating Rabbi Aaron Nathan Weiss zatzal. A preliminary version
appeared in Hatzofe, Erev Shabbat Bamidbar, Yom Shichrur Yerushalayim, 28
Iyar ha-tashnat; May 14, 1999. p. 14.
* A.S. Fraenkel, Kabalat ol malchut shamayim, in Hebrew. Morashteinu vol.
13, 33-38, Sept. 1999. Preliminaty version appeared in Hatzofe, Erev
Shabbat Vay'chi, 13 Teiveit ha-tashnat; January 1, 1999, p. 12.
* A.S. Fraenkel, K'az kein atah, in Hebrew. Hatzofe, Erev Pesach, 14 Nissan
ha-tashnat; March 31, 1999, p. 14.
* A.S. Fraenkel, Bameh maftirin uvameh ein maftirin, in Hebrew. Hatzofe,
Erev Shabbat Nitzavim-Vayeilech, 24 Elul ha-tashnaz; September 26, 1997,
pp. 7--8.
* A.S. Fraenkel, Madua ein korin korban musaf shel shabbat b'shabbat, in
Hebrew. Hatzofe, Erev Shabbat Pin'chas, 20 Tamuz ha-tashnaz; July 25,
1997, p. 6.
* A.S. Fraenkel, Hafradat rashuyot tifkudit bein kohen gadol, melech
v'sarim?, in Hebrew. Hatzofe, Erev Shabbat Acharei Mot, 25 Nissan
ha-tashnaz; May 2, 1997, p. 7.
* A.S. Fraenkel, Haramba"m, haRashb"a uMaran al ta'ut b'seifer Torah, in
Hebrew. Moriya 21 Issue 5--6, Adar Beit ha-tashnaz; 1997, pp. 109--110.
* A.S. Fraenkel, L'olam heveih adam koneis divrei Torah k'lalim, in Hebrew.
Hatzofe, Erev Shabbat Ki Tissa, 21 Adar Aleph ha-tashnaz; Feb. 28, 1997,
p. 8.
* A.S. Fraenkel, Nusach birkat "me'ein shalosh" utfilato shel kohen gadol
b'yom hakipurim, in Hebrew. Sh'ma'atin 125, Chanukah ha-tashnav; 1995, pp.
80-87.
GAMES BIBLIOGRAPHY
A dynamic bibliography on Combinatorial Games, currently containing over
1700 items is a Dynamic Survey (D2, originally 1994) in the Dynamic
Surveys section of the Electronic Journal of Combinatorics. For the latest
update, view/download one of the files: gb.dvi, gb.pdf. Corrections,
suggestions and comments are welcome. They should be sent to me by email.
ELECTRONIC JOURNALS
Some of the leading refereed electronic journals in mathematics can be
accessed from here, via the courtesy of the AMS. We mention especially the
influential Electr. J. Combinatorics, and the younger, yet prestigeous,
INTEGERS -- Electronic Journal of Combinatorial Number Theory. It has a
combinatorial games section.
THE RESPONSA STORAGE AND RETRIEVAL PROJECT
The Responsa Project stores the largest compilation of Jewish databases
(it should actually be considerably larger). The most sophisticated search
tools for Hebrew and Aramaic text processing (which should be much more
sophisticated!) have been developed for searching it. Its philosophy,
described from two viewpoints, can be found at: Yaacov Choueka, Aviezri
Fraenkel's Work in Information Retrieval and Related Areas, A.S. Fraenkel,
The Responsa storage and retrieval system---whither? The Hebrew version:
Proyect hashut: avar, hoveh---v'gam atid? appeared in Dinei Yisrael 19
(1997-98) 253--270. It is a full text storage and retrival system,
preceeding Google by 35 years, used worldwide. In 2007 it was awarded the
prestigious Israel Prize.
THE GOOD COUNTRIES AND THE GOOD PEOPLE THEREIN
* Australia: Rony Attar, Nhan Bao Ho, Jamie Simpson
* Belgium; Emilie Charlier, Michel Rigo
* Canada: Jason Bell, British Columbia; James Jones, Alberta; the late Anton
Kotzig, Quebec; Richard Nowakowski, Nova Scotia; Gert Sabidussi, Quebec
* China: Rudolf Fleischer, Haiyan Li, Sanyang Liu, Wen An Liu
* Czech Republic: Martin Loebl, Jaroslav Nesetril
* France; Eric Duchene, Sylvain Gravier
* Germany: Sandor Fekete, Matthias Schmitt
* Hungary: the late Paul Erdos, Vera Sos
* Israel: Zvia Agur, Shiri Artstein-Avidan, Alexander Barabash, Marc Berger,
Uri Blass, Viktor Bronstein, Yaacov Choueka, Meir Cohen, Nachum
Dershowitz, Joseph Dueck, N. Duvdevani, the late Joseph Gillis, Lior
Goldberg, Elisheva Goldschmidt, Romina Guelman, Ron Holzman, Tomi Klein,
Dalia Krieger, the late Dan Loewenthal, Mordechai Lorberbom, the late
Moshe Mor, Mordechai Mushkin, Michal Ozery, Udi Peled, Ofer Rahat, Benny
Reuter, D. Schindler, Tamar Seeman, E. Segal, the late Michael Shimshoni,
Mark Slae, E. Spitz, Yuval Tanny, Uzi Tassa, Barak Weiss, Sinai Yedid
(Responsa), Dmitri Zusman
* Italy: The late Alberto Apostolico
* Portugal: Carlos Santos
* Sweden: Peter Hegarty, Urban Larsson
* UK: Jonathan Levitt, Mike Paterson
* USA: George Andrews, PA, Saul Blanco, Itshak Borosh, TX; Michael
Boshernitzan, TX; the late David Cantor, CA; Philip J. Davis, RI; Erik
Demaine, MA; Roger Eggleton, IL; the late Gerald Estrin, CA; Alexander
Felzenbaum, NY; Alex Fink, NC; Michael Garey, NJ; the late Basil Gordon,
CA; Vladimir Gurvich, NJ; the late Peter Hammer, NJ; the late Frank
Harary, NM; Robert Hearn, CA, Hans Herda, MA; Alan Jaffrey, IL; David
Johnson, NJ; Joseph Kahane, NY; Clark Kimberling, IN; Alex Kontorovich,
NY; David Lichtenstein, MA; Yehoshua Perl, NJ; Horacio Porta, IL; D. Raab,
NY; Edward Reingold, IL; Elnatan Reisner, MD; Prashant Saxena, IL;Thomas
Schaefer, CA; Edward Scheinerman, MD; James Sellers, PA, Aaron Siegel, CA,
Shai Simonson, MA; Kenneth Stolarsky, IL; the late Ernst Straus, CA; the
late Rein Turn, CA; Daniel Ullman, DC; Yaacov Yesha, MD
VANITY OF VANITIES -- ALL IS VANITY (ECCL. 1,2)
2014, Medal of Honor World Orthodox Leadership Forum, for the Responsa
Project. Rabbi Avichai Katzin, from the awarding committee, wrote inter
alia (translation from Hebrew): "The establishment of an enterprise as
important as the Responsa Project, that daily grants many thousands the
study of Judaica at an outstanding scale, undoubtely deserves more than
the decoration you received."
2007, Elected Meritocrat of Rehovot (Yakir Ha'ir). One of the photos of
the ceremony, March 6, 2007. (without recipient and spouse)
2007, Israel Prize for the Responsa Project, initiated in 1963, that
appears to be the first viable, durable full-text retrieval system, 35
years prior to Google.
2006, Recipient of WEIZAC Medal, at December 5 special seminar,
celebrating recognition by the IEEE of the WEIZAC project as a Milestone
in the History of Computers. (WEIZAC, constructed at the Weizmann
Institute of Science in 1954, was the first electronic digital computer in
the Middle East, and one of the first in the world.)
2005, Euler Medal recipient of the Institute for Combinatorics and Its
Applications. Excerpts from the citation in Bull. ICA 47, May 2006; front
of medal, back; photographed by Eli Shechtman.
2005, Runner up in European Mathematical Society Article Competition.
2001, The Fraenkel Festschrift volume, Electr, J. of Combinatorics, vol.
8(2).
1998, Quality Initiative Citation to the Responsa Project for creative,
high-quality and visionary projects to celebrate the 50th anniversary of
the establishment of the State of Israel.
1972, Feder Foundation Prize for initiating and creating the Responsa
Project.
Wikipedia pages: Hebrew ; English ; German .
PERSONAL DATA
* Email: "aviezri.fraenkel" followed by the "at" symbol, followed by
"weizmann.ac.il" .
* Telephone: 972-8-9343539; secretary: 972-8-9343545
* Fax: 972-8-9342945.
* Business address:
* Professor Aviezri S. Fraenkel
* Dept of Compu Sci & Appl Math
* Weizmann Institute of Science
* 76100 Rehovot
* Israel
URL for this homepage is: http://www.wisdom.weizmann.ac.il/~fraenkel
Return for additional wisdom