Aviezri Siegmund Fraenkel - Author Profile

Edit Profile

Fraenkel, Aviezri Siegmund

Author ID:	fraenkel.aviezri-s
Published as:	Fraenkel, Aviezri S.; Fraenkel, A. S.; Fraenkel, Aviezri; Fränkel, A. S. more...less
Further Spellings:	אביעזרי פרנקל
Homepage:	http://www.wisdom.weizmann.ac.il/~fraenkel/
External Links:	MGP · Wikidata · dblp · GND

Documents Indexed:	177 Publications since 1961, including 2 Additional arXiv Preprints
	2 Contributions as Editor · 1 Further Contribution
Biographic References:	3 Publications
Co-Authors:	100 Co-Authors with 120 Joint Publications
	4,225 Co-Co-Authors

all top 5

Co-Authors

57	single-authored
16	Berger, Marc A.
16	Felzenbaum, Alexander
10	Simpson, Jamie
7	Larsson, Urban
6	Borosh, Itshak
6	Klein, Shmuel Tomi
6	Yesha, Yaacov
4	Tassa, Uzi
3	Duchêne, Eric
3	Mor, Moshe
3	Nowakowski, Richard Joseph
2	Agur, Zvia
2	Andrews, George Eyre
2	Attar, R.
2	Blass, Uri
2	Boshernitzan, Michael D.
2	Davis, Philip J.
2	Goldberg, Lior
2	Ho, Nhan Bao
2	Holzman, Ron
2	Kimberling, Clark H.
2	Kotzig, Anton
2	Lichtenstein, David
2	Loebl, Martin
2	Lorberbom, Mordechai
2	Nešetřil, Jaroslav
2	Porta, Horacio A.
2	Rigo, Michel
2	Santos, Carlos P.
2	Scheinerman, Edward R.
2	Sellers, James Allen
2	Stolarsky, Kenneth B.
2	Zeilberger, Doron
1	Alon, Noga
1	Apostolico, Alberto
1	Artstein-Avidan, Shiri
1	Barabash, Alexander
1	Bell, Jason P.
1	Blanco, Saúl A.
1	Bronstein, Victor
1	Calkin, Neil J.
1	Canfield, Rodney E.
1	Cantor, David Geoffrey
1	Charlier, Emilie
1	Choueka, Yaacov
1	Chung, Fan
1	Dershowitz, Nachum
1	Duvdevani, N.
1	Eggleton, Roger B.
1	Ekhad, Shalosh B. (computer)
1	Erdős, Pál
1	Estrin, Gerald
1	Fekete, Sándor P.
1	Fink, Alex
1	Fleischer, Rudolf
1	Goldschmidt, Elisheva
1	Golumbic, Martin Charles
1	Gordon, Basil
1	Gravier, Sylvain
1	Greene, Curtis
1	Guelman, Romina
1	Gulian, Mamikon
1	Gurvich, Vladimir A.
1	Hammer, Peter Ladislaw
1	Harary, Frank
1	Hegarty, Peter V.
1	Herda, Hans
1	Hutchinson, Joan P.
1	Jaffray, Alan
1	Kahane, Joseph
1	Knuth, Donald Ervin
1	Kontorovich, Alex V.
1	Krieger, Dalia
1	Lazebnik, Felix
1	Levitt, Jonathan
1	Li, Haiyan
1	Liu, Sanyang
1	Liu, Wenan
1	Loewenthal, Dan
1	Mushkin, Mordechai
1	Nijenhuis, Albert
1	Ozery, Michal
1	Paterson, Mike S.
1	Peled, Udi
1	Petkovšek, Marko
1	Rahat, O.
1	Reingold, Edward Martin
1	Reisner, Elnatan
1	Sabidussi, Gert
1	Savage, Carla Diane
1	Saxena, Prashant
1	Schmitt, Matthias
1	Seeman, Tamar
1	Shimshoni, Michael
1	Simonson, Shai
1	Sós, Vera Turán
1	Stanley, Richard Peter
1	Straus, Ernst G.
1	Swiler, Laura P.
1	Tanny, Yuval
...and 5 more Co-Authors

all top 5

Serials

19	Discrete Mathematics
15	Theoretical Computer Science
12	Journal of Combinatorial Theory. Series A
9	Discrete Applied Mathematics
8	American Mathematical Monthly
6	The Electronic Journal of Combinatorics
6	Integers
5	International Journal of Game Theory
4	Mathematics Magazine
4	Acta Arithmetica
4	The Computer Journal. Section A / Section B
3	Journal of the Association for Computing Machinery
3	Proceedings of the American Mathematical Society
3	Transactions of the American Mathematical Society
2	Computers & Mathematics with Applications
2	Information Processing Letters
2	Mathematics of Computation
2	Ars Combinatoria
2	Canadian Mathematical Bulletin
2	Pacific Journal of Mathematics
2	Notices of the American Mathematical Society
1	Computer Methods in Applied Mechanics and Engineering
1	IEEE Transactions on Information Theory
1	Mathematical Proceedings of the Cambridge Philosophical Society
1	Bulletin of Mathematical Biology
1	Canadian Journal of Mathematics
1	Colloquium Mathematicum
1	Fundamenta Mathematicae
1	Journal of Combinatorial Theory. Series B
1	Journal of Number Theory
1	Proceedings of the London Mathematical Society. Third Series
1	Journal of Algorithms
1	European Journal of Combinatorics
1	Combinatorica
1	Journal of Complexity
1	Algorithmica
1	Information and Computation
1	SIAM Journal on Discrete Mathematics
1	International Journal of Algebra and Computation
1	Bulletin of the American Mathematical Society. New Series
1	The Australasian Journal of Combinatorics
1	Random & Computational Dynamics
1	Annals of Combinatorics
1	International Journal of Pure and Applied Mathematics
1	Bulletin of the American Mathematical Society
1	Journal of the London Mathematical Society
1	Journal of Research of the National Bureau of Standards
1	The College Mathematics Journal
1	Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae

all top 5

Fields

84	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
64	Number theory (11-XX)
38	Combinatorics (05-XX)
38	Computer science (68-XX)
9	Information and communication theory, circuits (94-XX)
8	Numerical analysis (65-XX)
6	Operations research, mathematical programming (90-XX)
5	General and overarching topics; collections (00-XX)
5	Group theory and generalizations (20-XX)
4	Biology and other natural sciences (92-XX)
3	History and biography (01-XX)
2	Mathematical logic and foundations (03-XX)
2	Convex and discrete geometry (52-XX)
1	Field theory and polynomials (12-XX)
1	Real functions (26-XX)
1	Measure and integration (28-XX)
1	Functions of a complex variable (30-XX)
1	Special functions (33-XX)
1	Dynamical systems and ergodic theory (37-XX)
1	Geometry (51-XX)
1	Statistics (62-XX)
1	Statistical mechanics, structure of matter (82-XX)
1	Mathematics education (97-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

150 Publications have been cited 1,329 times in 782 Documents	Cited by ▼	Year ▼
Systems of numeration. Zbl 0568.10005 Fraenkel, Aviezri S.	93	1985
How many squares can a string contain? Zbl 0910.05001 Fraenkel, Aviezri S.; Simpson, Jamie	62	1998
How to beat your Wythoff games’ opponent on three fronts. Zbl 0504.90087 Fraenkel, Aviezri S.	44	1982
How many squares must a binary sequence contain? Zbl 0816.11007 Fraenkel, Aviezri S.; Simpson, R. Jamie	37	1995
The bracket function and complementary sets of integers. Zbl 0172.32501 Fraenkel, Aviezri S.	36	1969
Planar kernel and Grundy with \(d\leq 3\), \(dout\leq 2\), \(din\leq 2\) are NP- complete. Zbl 0493.68040 Fraenkel, Aviezri S.	32	1981
Extensions and restrictions of Wythoff’s game preserving its \(\mathcal P\) positions. Zbl 1185.91061 Duchêne, Eric; Fraenkel, Aviezri S.; Nowakowski, Richard J.; Rigo, Michel	31	2010
Complementing and exactly covering sequences. Zbl 0257.05023 Fraenkel, Aviezri S.	30	1973
Determination of \([n\theta]\) by its sequence of differences. Zbl 0401.10018 Fraenkel, Aviezri S.; Mushkin, M.; Tassa, Uzi	29	1978
Computing a perfect strategy for nxn chess requires time exponential in n. Zbl 0467.90100 Fraenkel, Aviezri S.; Lichtenstein, David	27	1981
Heap games, numeration systems and sequences. Zbl 0942.91015 Fraenkel, Aviezri S.	26	1998
Nimhoff games. Zbl 0748.90081 Fraenkel, Aviezri S.; Lorberbom, Mordechai	25	1991
The exact number of squares in Fibonacci words. Zbl 0916.68122 Fraenkel, Aviezri S.; Simpson, Jamie	23	1999
Complexity, appeal and challenges of combinatorial games. Zbl 1066.91017 Fraenkel, Aviezri S.	22	2004
Wythoff games, continued fractions, cedar trees and Fibonacci searches. Zbl 0557.90107 Fraenkel, Aviezri S.	21	1984
Complexity of problems in games, graphs and algebraic equations. Zbl 0429.90103 Fraenkel, Aviezri S.; Yesha, Yaacov	21	1979
Undirected edge geography. Zbl 0801.90147 Fraenkel, Aviezri S.; Scheinerman, Edward R.; Ullman, Daniel	19	1993
The number of fixed points of the majority rule. Zbl 0659.05004 Agur, Z.; Fraenkel, A. S.; Klein, S. T.	19	1988
Robust transmission of unbounded strings using Fibonacci representations. Zbl 0626.94007 Apostolico, Alberto; Fraenkel, Aviezri S.	17	1987
Combinatorial games: Selected bibliography with a succinct gourmet introduction. Zbl 0871.90147 Fraenkel, Aviezri S.	17	1997
A characterization of exactly covering congruences. Zbl 0257.10003 Fraenkel, Aviezri S.	16	1973
Combinatorial games: selected bibliography with a succinct gourmet introduction. Zbl 1062.91016 Fraenkel, Aviezri S.	15	2002
Cayley permutations. Zbl 0537.05028 Mor, Moshe; Fraenkel, Aviezri S.	15	1984
The Sprague-Grundy function for Wythoff’s game. Zbl 0701.68037 Blass, Uri; Fraenkel, Aviezri S.	14	1990
Robust universal complete codes for transmission and compression. Zbl 0874.94026 Fraenkel, Aviezri S.; Klein, Shmuel T.	14	1996
Characterization of the set of values \(f(n)=[n \alpha ], n=1,2,\dots \). Zbl 0246.10005 Fraenkel, Aviezri S.; Levitt, Jonathan; Shimshoni, Michael	14	1972
Another bridge between Nim and Wythoff. Zbl 1187.91031 Duchêne, E.; Fraenkel, A. S.; Gravier, S.; Nowakowski, R. J.	13	2009
Adjoining to Wythoff’s game its P-positions as moves. Zbl 0915.90291 Fraenkel, Aviezri S.; Ozery, Michal	13	1998
Geography. Zbl 0799.90145 Fraenkel, A. S.; Simonson, S.	12	1993
PSPACE-Hardness of some combinatorial games. Zbl 0619.90109 Fraenkel, Aviezri S.; Goldschmidt, Elisheva	12	1987
A non-analytic proof of the Newman-Znám result for disjoint covering systems. Zbl 0608.10006 Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.	12	1986
A linear algorithm for nonhomogeneous spectra of numbers. Zbl 0555.65008 Boshernitzan, M.; Fraenkel, Aviezri S.	12	1984
A generalization of Jarnik’s theorem on Diophantine approximations. Zbl 0242.10014 Borosh, I.; Fraenkel, Aviezri S.	12	1972
Euclid and Wythoff games. Zbl 1079.91011 Fraenkel, Aviezri S.	12	2005
Harnessing the unwieldy MEX function. Zbl 1405.91081 Fraenkel, Aviezri S.; Peled, Udi	12	2015
Invariant and dual subtraction games resolving the Duchêne-Rigo conjecture. Zbl 1237.91062 Larsson, Urban; Hegarty, Peter; Fraenkel, Aviezri S.	11	2011
Complexity of protein folding. Zbl 0791.92010 Fraenkel, Aviezri S.	11	1993
Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups. Zbl 0808.05008 Fraenkel, Aviezri S.	11	1994
Exact solutions of linear equations with rational coefficients by congruence techniques. Zbl 0137.11002 Borosh, I.; Fraenkel, Aviezri S.	11	1966
Nonhomogeneous spectra of numbers. Zbl 0456.10005 Boshernitzan, M.; Fraenkel, Aviezri S.	11	1981
A generalization of Wythoff’s game. Zbl 0265.90065 Fraenkel, Aviezri S.; Borosh, I.	11	1973
Characterizing the number of \(m\)-ary partitions modulo \(m\). Zbl 1342.05013 Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James A.	11	2015
Remark on the multiplicity of a partition of a group into cosets. Zbl 0652.20030 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri	10	1987
Combinatorial game theory foundations applied to digraph kernels. Zbl 0884.05045 Fraenkel, Aviezri S.	10	1997
The generalized Sprague-Grundy function and its invariance under certain mappings. Zbl 0622.05030 Fraenkel, Aviezri S.; Yesha, Yaacov	9	1986
On the determination of sets by the sets of sums of a certain order. Zbl 0104.27003 Gordon, B.; Fraenkel, Aviezri S.; Straus, E. G.	9	1962
Theory of annihilation games. I. Zbl 0493.90099 Fraenkel, Aviezri S.; Yesha, Yaacov	9	1982
Theory of annihilation games. Zbl 0331.05112 Fraenkel, Aviezri S.; Yesha, Yaacov	8	1976
The vile, dopey, evil and odious game players. Zbl 1231.91046 Fraenkel, Aviezri S.	8	2012
Some arithmetical semigroups. Zbl 0728.11034 Fraenkel, A. S.; Porta, H.; Stolarsky, K. B.	8	1990
A deletion game on hypergraphs. Zbl 0728.90106 Fraenkel, Aviezri S.; Scheinerman, Edward R.	8	1991
Scenic trails ascending from Sea-level Nim to Alpine Chess. Zbl 0872.90136 Fraenkel, Aviezri S.	8	1997
Gap problems for integer part and fractional part sequences. Zbl 0822.11021 Fraenkel, Aviezri S.; Holzman, Ron	8	1995
The Herzog-Schönheim conjecture for finite nilpotent groups. Zbl 0553.20009 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri	8	1986
New games related to old and new sequences. Zbl 1089.11017 Fraenkel, Aviezri S.	8	2004
Constructions in combinatorial games with cycles. Zbl 0332.90053 Fraenkel, Aviezri S.; Perl, Y.	8	1975
The Rat game and the Mouse game. Zbl 1380.91043 Fraenkel, Aviezri S.	8	2015
The game of End-Wythoff. Zbl 1192.91053 Fraenkel, Aviezri S.; Reisner, Elnatan	7	2009
Lattice parallelotopes and disjoint covering systems. Zbl 0623.10003 Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.	7	1987
Combinatorial games: Selected bibliography with a succinct gourmet introduction. Zbl 0977.91009 Fraenkel, Aviezri S.	7	1996
Improvements to two results concerning systems of residue sets. Zbl 0587.05023 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	7	1985
Disjoint covering systems of rational Beatty sequences. Zbl 0589.10060 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	7	1986
New results for covering systems of residue sets. Zbl 0589.10061 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	7	1986
Strategy for a class of games with dynamic ties. Zbl 0348.90177 Fraenkel, Aviezri S.; Tassa, Uzi	7	1975
Complementary systems of integers. Zbl 0359.10048 Fraenkel, Aviezri S.	7	1977
Aperiodic subtraction games. Zbl 1237.91061 Fraenkel, Aviezri S.	6	2011
A new heap game. Zbl 0986.91002 Fraenkel, A. S.; Zusman, D.	6	2001
Complexity aspects of guessing prefix codes. Zbl 0844.94008 Fraenkel, A. S.; Klein, S. T.	6	1994
Two-player games on cellular automata. Zbl 1109.91324 Fraenkel, Aviezri S.	6	2002
Gaussian process regression constrained by boundary value problems. Zbl 1507.62232 Gulian, M.; Frankel, A.; Swiler, L.	6	2022
Permutation generation on vector processors. Zbl 0491.68060 Mor, Moshe; Fraenkel, Aviezri S.	6	1982
Complexity of solving algebraic equations. Zbl 0487.68036 Fraenkel, Aviezri S.; Yesha, Yaacov	6	1980
Traveling salesmen in the presence of competition. Zbl 1067.90139 Fekete, Sándor P.; Fleischer, Rudolf; Fraenkel, Aviezri; Schmitt, Matthias	6	2004
A class of Wythoff-like games. Zbl 1332.91031 Fraenkel, Aviezri; Tanny, Yuval	6	2013
\(m\)-ary partitions with no gaps: a characterization modulo \(m\). Zbl 1322.05015 Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James A.	6	2016
Bidirectional Huffman coding. Zbl 1373.94859 Fraenkel, A. S.; Klein, S. T.	6	1990
The Raleigh game. Zbl 1178.91037 Fraenkel, Aviezri S.	5	2007
A two-parameter family of an extension of Beatty sequences. Zbl 1194.11030 Artstein-Avidan, Shiri; Fraenkel, Aviezri S.; Sós, Vera T.	5	2008
Pseudo-Boolean functions and their graphs. Zbl 0557.94019 Fraenkel, Aviezri S.; Hammer, Peter L.	5	1984
How far can nim in disguise be stretched? Zbl 0913.90288 Blass, Uri; Fraenkel, Aviezri S.; Guelman, Romina	5	1998
Computing a perfect strategy for nxn chess requires time exponential in N. Zbl 0462.68090 Fraenkel, Aviezri S.; Lichtenstein, David	5	1981
Partizan octal games: Partizan subtraction games. Zbl 0662.90095 Fraenkel, A. S.; Kotzig, A.	5	1987
Complementary iterated floor words and the Flora game. Zbl 1250.91023 Fraenkel, Aviezri S.	4	2010
A decision problem for ultimately periodic sets in nonstandard numeration systems. Zbl 1194.68131 Bell, Jason; Charlier, Emilie; Fraenkel, Aviezri S.; Rigo, Michel	4	2009
The use and usefulness of numeration systems. Zbl 0672.10008 Fraenkel, Aviezri S.	4	1989
Necessary condition for the existence of an incongruent covering system with odd moduli. II. Zbl 0623.10004 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	4	1987
k-Welter - a generalization of Welter’s game. Zbl 0617.90088 Kahane, Joseph; Fraenkel, Aviezri S.	4	1987
Epidemiography. II: Games with a dozing yet winning player. Zbl 0649.90110 Fraenkel, Aviezri S.; Loebl, Martin; Nešetřil, Jaroslav	4	1988
Geodetic contraction games on graphs. Zbl 0678.90098 Fraenkel, A. S.; Harary, F.	4	1989
Wythoff visions. Zbl 1444.91055 Duchêne, Eric; Fraenkel, Aviezri S.; Gurvich, Vladimir; Ho, Nhan Bao; Kimberling, Clark; Larsson, Urban	4	2019
Epidemiography. Zbl 0574.90110 Fraenkel, Aviezri S.; Nešetřil, Jaroslav	4	1985
Combinatorial games with an annihilation rule. Zbl 0284.90088 Fraenkel, Aviezri S.	4	1974
Restrictions of \(m\)-Wythoff Nim and \(p\)-complementary Beatty sequences. Zbl 1380.91047 Larsson, Urban	4	2015
Games on arbitrarily large rats and playability. Zbl 1460.91053 Fraenkel, Aviezri S.; Larsson, Urban	3	2019
Covers of product sets and the Korec-Znám result. Zbl 0645.10048 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
Disjoint covering systems with precisely one multiple modulus. Zbl 0647.10005 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
Mycielski-Sierpiński conjecture and Korec-Znám result. Zbl 0677.20019 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
On infinite and finite covering systems. Zbl 0743.11005 Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.; Holzman, R.	3	1991
On infinite disjoint covering systems. Zbl 0784.05011 Fraenkel, Aviezri S.; Simpson, R. Jamie	3	1993
Generalized Wythoff arrays, shuffles and interspersions. Zbl 0793.05050 Fraenkel, A. S.; Kimberling, Clark	3	1994
Gaussian process regression constrained by boundary value problems. Zbl 1507.62232 Gulian, M.; Frankel, A.; Swiler, L.	6	2022
Wythoff visions. Zbl 1444.91055 Duchêne, Eric; Fraenkel, Aviezri S.; Gurvich, Vladimir; Ho, Nhan Bao; Kimberling, Clark; Larsson, Urban	4	2019
Games on arbitrarily large rats and playability. Zbl 1460.91053 Fraenkel, Aviezri S.; Larsson, Urban	3	2019
Variants of \((s, t)\)-Wythoff’s game. Zbl 1367.91042 Li, Haiyan; Liu, Sanyang; Fraenkel, Aviezri S.; Liu, Wen An	3	2017
\(m\)-ary partitions with no gaps: a characterization modulo \(m\). Zbl 1322.05015 Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James A.	6	2016
Harnessing the unwieldy MEX function. Zbl 1405.91081 Fraenkel, Aviezri S.; Peled, Udi	12	2015
Characterizing the number of \(m\)-ary partitions modulo \(m\). Zbl 1342.05013 Andrews, George E.; Fraenkel, Aviezri S.; Sellers, James A.	11	2015
The Rat game and the Mouse game. Zbl 1380.91043 Fraenkel, Aviezri S.	8	2015
Restrictions of \(m\)-Wythoff Nim and \(p\)-complementary Beatty sequences. Zbl 1380.91047 Larsson, Urban	4	2015
When are translations of \(\mathcal P\)-positions of Wythoff’s game \(\mathcal P\)-positions? Zbl 1371.91030 Fraenkel, Aviezri S.; Ho, Nhan Bao	1	2015
Combinatorial games: selected short bibliography with a succinct gourmet introduction. Zbl 1380.91044 Fraenkel, Aviezri S.; Nowakowski, Richard J.	1	2015
Herbert S. Wilf (1931–2012). Zbl 1338.01033 Knuth, Donald E.; Fraenkel, Aviezri S.; Zeilberger, Doron; Petkovšek, Marko; Calkin, Neil; Canfield, Rodney; Nijenhuis, Albert; Savage, Carla D.; Stanley, Richard P.; Lazebnik, Felix	1	2015
Corrigendum to: “The exact number of squares in Fibonacci words”. Zbl 1303.68098 Fraenkel, Aviezri S.; Simpson, Jamie	2	2014
LIM is not slim. Zbl 1294.91039 Fink, Alex; Fraenkel, Aviezri S.; Santos, Carlos	1	2014
A class of Wythoff-like games. Zbl 1332.91031 Fraenkel, Aviezri; Tanny, Yuval	6	2013
Beating your fractional Beatty game opponent and: what’s the question to your answer? Zbl 1278.91030 Fraenkel, Aviezri S.	1	2013
The vile, dopey, evil and odious game players. Zbl 1231.91046 Fraenkel, Aviezri S.	8	2012
Invariant and dual subtraction games resolving the Duchêne-Rigo conjecture. Zbl 1237.91062 Larsson, Urban; Hegarty, Peter; Fraenkel, Aviezri S.	11	2011
Aperiodic subtraction games. Zbl 1237.91061 Fraenkel, Aviezri S.	6	2011
Extensions and restrictions of Wythoff’s game preserving its \(\mathcal P\) positions. Zbl 1185.91061 Duchêne, Eric; Fraenkel, Aviezri S.; Nowakowski, Richard J.; Rigo, Michel	31	2010
Complementary iterated floor words and the Flora game. Zbl 1250.91023 Fraenkel, Aviezri S.	4	2010
From enmity to amity. Zbl 1220.11033 Fraenkel, Aviezri S.	1	2010
Another bridge between Nim and Wythoff. Zbl 1187.91031 Duchêne, E.; Fraenkel, A. S.; Gravier, S.; Nowakowski, R. J.	13	2009
The game of End-Wythoff. Zbl 1192.91053 Fraenkel, Aviezri S.; Reisner, Elnatan	7	2009
A decision problem for ultimately periodic sets in nonstandard numeration systems. Zbl 1194.68131 Bell, Jason; Charlier, Emilie; Fraenkel, Aviezri S.; Rigo, Michel	4	2009
A two-parameter family of an extension of Beatty sequences. Zbl 1194.11030 Artstein-Avidan, Shiri; Fraenkel, Aviezri S.; Sós, Vera T.	5	2008
The Raleigh game. Zbl 1178.91037 Fraenkel, Aviezri S.	5	2007
The Sierpiński sieve of Nim-varieties and binomial coefficients. Zbl 1178.11020 Fraenkel, Aviezri S.; Kontorovich, Alex	2	2007
Euclid and Wythoff games. Zbl 1079.91011 Fraenkel, Aviezri S.	12	2005
Complexity, appeal and challenges of combinatorial games. Zbl 1066.91017 Fraenkel, Aviezri S.	22	2004
New games related to old and new sequences. Zbl 1089.11017 Fraenkel, Aviezri S.	8	2004
Traveling salesmen in the presence of competition. Zbl 1067.90139 Fekete, Sándor P.; Fleischer, Rudolf; Fraenkel, Aviezri; Schmitt, Matthias	6	2004
The structure of complementary sets of integers: a 3-shift theorem. Zbl 1048.11019 Fraenkel, Aviezri S.; Krieger, Dalia	2	2004
Combinatorial games: selected bibliography with a succinct gourmet introduction. Zbl 1062.91016 Fraenkel, Aviezri S.	15	2002
Two-player games on cellular automata. Zbl 1109.91324 Fraenkel, Aviezri S.	6	2002
Arrays, numeration systems and Frankenstein games. Zbl 1002.91009 Fraenkel, Aviezri S.	2	2002
A new heap game. Zbl 0986.91002 Fraenkel, A. S.; Zusman, D.	6	2001
Virus versus mankind. Zbl 1001.91010 Fraenkel, Aviezri S.	3	2001
Infinite cyclic impartial games. Zbl 0976.91008 Fraenkel, A. S.; Rahat, O.	2	2001
The subword complexity of a two-parameter family of sequences. Zbl 0981.68125 Fraenkel, Aviezri S.; Seeman, Tamar; Simpson, Jamie	2	2001
An extension of the periodicity lemma to longer periods (invited lecture). Zbl 0990.68105 Fraenkel, Aviezri S.; Simpson, Jamie	2	2001
Recent results and questions in combinatorial game complexities. Zbl 0977.91011 Fraenkel, A. S.	2	2000
On the recurrence \(f_{m+1}=b_m f_m-f_{m-1}\) and applications. Zbl 0967.30003 Fraenkel, Aviezri S.	2	2000
The exact number of squares in Fibonacci words. Zbl 0916.68122 Fraenkel, Aviezri S.; Simpson, Jamie	23	1999
How many squares can a string contain? Zbl 0910.05001 Fraenkel, Aviezri S.; Simpson, Jamie	62	1998
Heap games, numeration systems and sequences. Zbl 0942.91015 Fraenkel, Aviezri S.	26	1998
Adjoining to Wythoff’s game its P-positions as moves. Zbl 0915.90291 Fraenkel, Aviezri S.; Ozery, Michal	13	1998
How far can nim in disguise be stretched? Zbl 0913.90288 Blass, Uri; Fraenkel, Aviezri S.; Guelman, Romina	5	1998
Combinatorial games: Selected bibliography with a succinct gourmet introduction. Zbl 0871.90147 Fraenkel, Aviezri S.	17	1997
Combinatorial game theory foundations applied to digraph kernels. Zbl 0884.05045 Fraenkel, Aviezri S.	10	1997
Scenic trails ascending from Sea-level Nim to Alpine Chess. Zbl 0872.90136 Fraenkel, Aviezri S.	8	1997
Error-correcting codes derived from combinatorial games. Zbl 0867.94030 Fraenkel, Aviezri S.	3	1997
Robust universal complete codes for transmission and compression. Zbl 0874.94026 Fraenkel, Aviezri S.; Klein, Shmuel T.	14	1996
Combinatorial games: Selected bibliography with a succinct gourmet introduction. Zbl 0977.91009 Fraenkel, Aviezri S.	7	1996
How many squares must a binary sequence contain? Zbl 0816.11007 Fraenkel, Aviezri S.; Simpson, R. Jamie	37	1995
Gap problems for integer part and fractional part sequences. Zbl 0822.11021 Fraenkel, Aviezri S.; Holzman, Ron	8	1995
Complexities of winning strategies in diophantine games. Zbl 0844.90141 Jones, J. P.; Fraenkel, A. S.	3	1995
Modular Nim. Zbl 0874.90225 Fraenkel, Aviezri S.; Jaffray, Alan; Kotzig, Anton; Sabidussi, Gert	2	1995
Iterated floor function, algebraic numbers, discrete chaos, Beatty subsequences, semigroups. Zbl 0808.05008 Fraenkel, Aviezri S.	11	1994
Complexity aspects of guessing prefix codes. Zbl 0844.94008 Fraenkel, A. S.; Klein, S. T.	6	1994
Generalized Wythoff arrays, shuffles and interspersions. Zbl 0793.05050 Fraenkel, A. S.; Kimberling, Clark	3	1994
Even kernels. Zbl 0813.68142 Fraenkel, Aviezri	2	1994
The almost PV behavior of some far from PV algebraic integers. Zbl 0811.11064 Fraenkel, A. S.; Porta, H.; Stolarsky, K. B.	1	1994
Undirected edge geography. Zbl 0801.90147 Fraenkel, Aviezri S.; Scheinerman, Edward R.; Ullman, Daniel	19	1993
Geography. Zbl 0799.90145 Fraenkel, A. S.; Simonson, S.	12	1993
Complexity of protein folding. Zbl 0791.92010 Fraenkel, Aviezri S.	11	1993
On infinite disjoint covering systems. Zbl 0784.05011 Fraenkel, Aviezri S.; Simpson, R. Jamie	3	1993
Beatty sequences and Langford sequences. Zbl 0790.11016 Eggleton, Roger B.; Fraenkel, Aviezri S.; Simpson, R. Jamie	2	1993
Bounding the depth of search trees. Zbl 1373.94951 Fraenkel, A. S.; Klein, S. T.	2	1993
Combinatorics and algorithms. Zbl 0783.00025	1	1993
Nimhoff games. Zbl 0748.90081 Fraenkel, Aviezri S.; Lorberbom, Mordechai	25	1991
A deletion game on hypergraphs. Zbl 0728.90106 Fraenkel, Aviezri S.; Scheinerman, Edward R.	8	1991
On infinite and finite covering systems. Zbl 0743.11005 Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.; Holzman, R.	3	1991
Selected bibliography on combinatorial games and some related material. Zbl 0726.90109 Fraenkel, Aviezri S.	1	1991
Complexity of games. Zbl 0753.90096 Fraenkel, Aviezri S.	1	1991
The Sprague-Grundy function for Wythoff’s game. Zbl 0701.68037 Blass, Uri; Fraenkel, Aviezri S.	14	1990
Some arithmetical semigroups. Zbl 0728.11034 Fraenkel, A. S.; Porta, H.; Stolarsky, K. B.	8	1990
Bidirectional Huffman coding. Zbl 1373.94859 Fraenkel, A. S.; Klein, S. T.	6	1990
Irreducible disjoint covering systems (with an application to Boolean algebra). Zbl 0729.11006 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	1	1990
The use and usefulness of numeration systems. Zbl 0672.10008 Fraenkel, Aviezri S.	4	1989
Geodetic contraction games on graphs. Zbl 0678.90098 Fraenkel, A. S.; Harary, F.	4	1989
Properties of k-Welter’s game. Zbl 0675.90096 Duvdevani, N.; Fraenkel, A. S.	2	1989
Epidemiography with various growth functions. Zbl 0677.90091 Fraenkel, Aviezri S.; Lorberbom, Mordechai	2	1989
Errata to: The number of fixed points of the majority rule. Zbl 0698.05006 Agur, Z.; Fraenkel, A. S.; Klein, S. T.	1	1989
The number of fixed points of the majority rule. Zbl 0659.05004 Agur, Z.; Fraenkel, A. S.; Klein, S. T.	19	1988
Epidemiography. II: Games with a dozing yet winning player. Zbl 0649.90110 Fraenkel, Aviezri S.; Loebl, Martin; Nešetřil, Jaroslav	4	1988
Covers of product sets and the Korec-Znám result. Zbl 0645.10048 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
Disjoint covering systems with precisely one multiple modulus. Zbl 0647.10005 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
Mycielski-Sierpiński conjecture and Korec-Znám result. Zbl 0677.20019 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
Improvements to the Newman-Znám result for disjoint covering systems. Zbl 0551.10003 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	3	1988
Robust transmission of unbounded strings using Fibonacci representations. Zbl 0626.94007 Apostolico, Alberto; Fraenkel, Aviezri S.	17	1987
PSPACE-Hardness of some combinatorial games. Zbl 0619.90109 Fraenkel, Aviezri S.; Goldschmidt, Elisheva	12	1987
Remark on the multiplicity of a partition of a group into cosets. Zbl 0652.20030 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri	10	1987
Lattice parallelotopes and disjoint covering systems. Zbl 0623.10003 Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.	7	1987
Partizan octal games: Partizan subtraction games. Zbl 0662.90095 Fraenkel, A. S.; Kotzig, A.	5	1987
Necessary condition for the existence of an incongruent covering system with odd moduli. II. Zbl 0623.10004 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri S.	4	1987
k-Welter - a generalization of Welter’s game. Zbl 0617.90088 Kahane, Joseph; Fraenkel, Aviezri S.	4	1987
A non-analytic proof of the Newman-Znám result for disjoint covering systems. Zbl 0608.10006 Berger, M. A.; Felzenbaum, A.; Fraenkel, A. S.	12	1986
The generalized Sprague-Grundy function and its invariance under certain mappings. Zbl 0622.05030 Fraenkel, Aviezri S.; Yesha, Yaacov	9	1986
The Herzog-Schönheim conjecture for finite nilpotent groups. Zbl 0553.20009 Berger, Marc A.; Felzenbaum, Alexander; Fraenkel, Aviezri	8	1986
...and 50 more Documents

all cited Publications top 5 cited Publications

all top 5

Cited by 1,044 Authors

62	Fraenkel, Aviezri Siegmund
21	Galeana-Sánchez, Hortensia
20	Rigo, Michel
18	Shallit, Jeffrey Outlaw
15	Rytter, Wojciech
14	Klein, Shmuel Tomi
14	Liu, Wenan
14	Radoszewski, Jakub
14	Simpson, Jamie
13	Waleń, Tomasz
12	Duchêne, Eric
10	Crochemore, Maxime
10	Frougny, Christiane
10	Gurvich, Vladimir A.
10	Sanchez-Lopez, Rocio
10	Shapira, Dana
9	Kociumaka, Tomasz
8	Blanchet-Sadri, Francine
8	Larsson, Urban
7	Chuan, Waifong
7	Franek, Frantisek
7	Glen, Amy
7	Ho, Nhan Bao
7	Li, Haiyan
7	Mercaş, Robert George
7	Nowakowski, Richard Joseph
6	Berger, Marc A.
6	Berthé, Valérie
6	Boros, Endre
6	Deza, Antoine
6	Felzenbaum, Alexander
6	Iliopoulos, Costas S.
6	Kimberling, Clark H.
6	Restivo, Antonio
5	Ilie, Lucian
5	Liu, Sanyang
5	Mantaci, Sabrina
5	Ochem, Pascal
5	Porubsky, Stefan
5	Puzynina, Svetlana
5	Smyth, William F.
5	Tichy, Robert Franz
5	Yesha, Yaacov
4	Allouche, Jean-Paul Simon
4	Andrews, George Eyre
4	Aragona, Riccardo
4	Badkobeh, Golnaz
4	Cerbai, Giulio
4	Chouraqui, Fabienne
4	Civino, Roberto
4	Dekking, Frederik Michel
4	Fekete, Sándor P.
4	Fici, Gabriele
4	Hernández-Cruz, César
4	Kapoor, Kalpesh
4	Kärki, Tomi
4	Li, Shuo
4	Locke, Stephen C.
4	Low, Richard M.
4	Messaoudi, Ali
4	Miller, Steven J.
4	Parreau, Aline
4	Patawar, Maithilee
4	Rampersad, Narad
4	Rao, Michaël
4	Stolarsky, Kenneth B.
4	Wu, Yaokun
4	Zhao, Xiao
3	Barcucci, Elena
3	Blidia, Mostafa
3	Bugeaud, Yann
3	Chan, Wai-hong
3	Charalampopoulos, Panagiotis
3	Charlier, Emilie
3	Claesson, Anders
3	Currie, James D.
3	Demaine, Erik D.
3	Fazekas, Szilárd Zsolt
3	Fleischer, Rudolf
3	Flocchini, Paola
3	Giambruno, Laura
3	Grabner, Peter J.
3	Gravier, Sylvain
3	Harju, Tero
3	Irie, Yuki
3	Kim, Dae San
3	Kim, Taekyun
3	Klavžar, Sandi
3	Komatsu, Takao
3	Kotlyarov, Nikita V.
3	Kubica, Marcin
3	Külekci, Muhammed Oğuzhan
3	Lagarias, Jeffrey C.
3	Matsumoto, Naoki
3	Mignosi, Filippo
3	Mousavi, Hamoon
3	Pissis, Solon P.
3	Pongsriiam, Prapanpong
3	Reif, John H.
3	Rojas-Monroy, Rocío
...and 944 more Authors

all top 5

Cited in 174 Serials

124	Theoretical Computer Science
66	Discrete Applied Mathematics
58	Discrete Mathematics
17	Journal of Combinatorial Theory. Series A
17	Journal of Number Theory
17	The Electronic Journal of Combinatorics
15	Integers
14	Information Processing Letters
13	European Journal of Combinatorics
12	Advances in Applied Mathematics
11	International Journal of Game Theory
10	Journal de Théorie des Nombres de Bordeaux
9	Journal of Computer and System Sciences
9	Proceedings of the American Mathematical Society
9	Information and Computation
9	RAIRO. Theoretical Informatics and Applications
8	Graphs and Combinatorics
8	Journal of Integer Sequences
7	RAIRO. Theoretical Informatics and Applications
6	Bulletin of the Australian Mathematical Society
6	Computers & Mathematics with Applications
6	Mathematica Slovaca
6	International Journal of Foundations of Computer Science
5	Transactions of the American Mathematical Society
5	Algorithmica
5	The Australasian Journal of Combinatorics
5	Journal of Discrete Algorithms
5	AKCE International Journal of Graphs and Combinatorics
4	Artificial Intelligence
4	BIT
4	Journal of Computational and Applied Mathematics
4	International Journal of Algebra and Computation
4	International Journal of Computer Mathematics
4	Cybernetics and Systems Analysis
4	Discussiones Mathematicae. Graph Theory
4	The Ramanujan Journal
4	Annals of Combinatorics
3	Mathematics of Computation
3	Monatshefte für Mathematik
3	Ergodic Theory and Dynamical Systems
3	Journal of Symbolic Computation
3	Applied Mathematics Letters
3	Indagationes Mathematicae. New Series
3	Chaos
3	Algorithms
2	American Mathematical Monthly
2	Israel Journal of Mathematics
2	Journal of Mathematical Analysis and Applications
2	Moscow University Mathematics Bulletin
2	Bulletin of Mathematical Biology
2	Acta Arithmetica
2	Advances in Mathematics
2	Annales de l’Institut Fourier
2	Canadian Mathematical Bulletin
2	Computing
2	The Fibonacci Quarterly
2	Journal of Soviet Mathematics
2	Results in Mathematics
2	Combinatorica
2	SIAM Journal on Discrete Mathematics
2	Linear Algebra and its Applications
2	Applied and Computational Harmonic Analysis
2	Journal of Mathematical Sciences (New York)
2	Journal of Difference Equations and Applications
2	Theory of Computing Systems
2	Journal of Combinatorial Optimization
2	Journal of the European Mathematical Society (JEMS)
2	RAIRO. Operations Research
2	Entropy
2	Chebyshevskiĭ Sbornik
2	Mathematics in Computer Science
2	International Journal of Combinatorics
2	Transactions on Combinatorics
2	JSIAM Letters
2	Open Mathematics
2	Research in Number Theory
1	International Journal of Modern Physics B
1	Communications in Algebra
1	Communications in Mathematical Physics
1	Computer Physics Communications
1	Indian Journal of Pure & Applied Mathematics
1	International Journal of Systems Science
1	Journal of Statistical Physics
1	Mathematical Proceedings of the Cambridge Philosophical Society
1	Mathematische Semesterberichte
1	Periodica Mathematica Hungarica
1	Problems of Information Transmission
1	Chaos, Solitons and Fractals
1	Mathematics Magazine
1	Beiträge zur Algebra und Geometrie
1	Annali di Matematica Pura ed Applicata. Serie Quarta
1	Applied Mathematics and Computation
1	Automatica
1	Czechoslovak Mathematical Journal
1	Functiones et Approximatio. Commentarii Mathematici
1	Fuzzy Sets and Systems
1	Information Sciences
1	Journal of Algebra
1	Journal of Combinatorial Theory. Series B
1	Journal of Pure and Applied Algebra
...and 74 more Serials

all top 5

Cited in 47 Fields

358	Computer science (68-XX)
249	Number theory (11-XX)
190	Combinatorics (05-XX)
190	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
36	Information and communication theory, circuits (94-XX)
27	Dynamical systems and ergodic theory (37-XX)
21	Group theory and generalizations (20-XX)
19	Operations research, mathematical programming (90-XX)
17	Numerical analysis (65-XX)
13	Mathematical logic and foundations (03-XX)
12	Convex and discrete geometry (52-XX)
11	Measure and integration (28-XX)
10	Order, lattices, ordered algebraic structures (06-XX)
10	Biology and other natural sciences (92-XX)
8	Probability theory and stochastic processes (60-XX)
7	Harmonic analysis on Euclidean spaces (42-XX)
5	Commutative algebra (13-XX)
5	Linear and multilinear algebra; matrix theory (15-XX)
4	Special functions (33-XX)
3	Geometry (51-XX)
3	General topology (54-XX)
3	Systems theory; control (93-XX)
2	General and overarching topics; collections (00-XX)
2	Associative rings and algebras (16-XX)
2	Category theory; homological algebra (18-XX)
2	Topological groups, Lie groups (22-XX)
2	Real functions (26-XX)
2	Partial differential equations (35-XX)
2	Difference and functional equations (39-XX)
2	Calculus of variations and optimal control; optimization (49-XX)
2	Manifolds and cell complexes (57-XX)
2	Statistics (62-XX)
2	Quantum theory (81-XX)
2	Statistical mechanics, structure of matter (82-XX)
2	Mathematics education (97-XX)
1	History and biography (01-XX)
1	General algebraic systems (08-XX)
1	Field theory and polynomials (12-XX)
1	Algebraic geometry (14-XX)
1	Nonassociative rings and algebras (17-XX)
1	Ordinary differential equations (34-XX)
1	Integral transforms, operational calculus (44-XX)
1	Functional analysis (46-XX)
1	Operator theory (47-XX)
1	Differential geometry (53-XX)
1	Fluid mechanics (76-XX)
1	Optics, electromagnetic theory (78-XX)

Citations by Year

Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.