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## Zeilberger, Doron

Compute Distance To:
 Author ID: zeilberger.doron Published as: Zeilberger, D.; Zeilberger, Doron Homepage: http://www.math.rutgers.edu/~zeilberg/ External Links: MGP · Wikidata · dblp · GND
 Documents Indexed: 229 Publications since 1971, including 1 Book
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#### Co-Authors

 96 single-authored 16 Ekhad, Shalosh B. (computer) 11 Foata, Dominique C. 8 Kauers, Manuel 8 Wilf, Herbert S. 5 Apagodu, Moa 5 Bressoud, David M. 5 Gillis, Joseph E. 4 Amdeberhan, Tewodros 4 Regev, Amitai 4 Robertson, Aaron 3 Janson, Svante 3 Koutschan, Christoph 3 Nakamura, Brian 3 Petkovšek, Marko 3 Sills, Andrew V. 2 Ayyer, Arvind 2 Canfield, E. Rodney 2 Chen, William Yong-Chuan 2 Friedman, Jane E. 2 Georgiadis, Evangelos 2 Gessel, Ira Martin 2 Gnang, Edinah K. 2 Hou, Qinghu 2 Jedwab, Jonathan 2 Mohammed, Mohamud 2 Noonan, John 2 Reznick, Bruce 2 Rowland, Eric S. 2 Savage, Carla D. 2 Thanatipanonda, Thotsaporn (Aek) 2 Wimp, Jet 2 Yang, Mingjia 2 Yao, Yukun 2 Zaleski, Anthony 1 Ahlgren, Scott D. 1 Almkvist, Gert 1 Andrews, George Eyre 1 Applegate, David L. 1 Bahturin, Yuri 1 Baxter, Andrew M. 1 Bender, Edward A. 1 Benjamin, Arthur T. 1 Berenstein, Arkady 1 Calkin, Neil J. 1 Canfield, Rodney E. 1 Caplan, S. Roy 1 Chamberland, Marc 1 Chung Graham, Fan-Rong King 1 Cooper, Bobbe J. 1 Corteel, Sylvie 1 Dym, Harry 1 Edlin, Anne E. 1 Fraenkel, Aviezri Siegmund 1 Franzblau, Deborah S. 1 Garoufalidis, Stavros 1 Greene, Curtis 1 Hogan, Emilie 1 Hutchinson, Joan P. 1 Knuth, Donald Ervin 1 Krattenthaler, Christian Friedrich 1 Kung, Joseph P. S. 1 Lazebnik, Felix 1 Le, Thang Tu Quoc 1 Lohr, Andrew 1 Medina, Luis A. 1 Mu, Yanping 1 Nemes, István 1 Nicholson, Daniel J. 1 Nijenhuis, Albert 1 Ono, Ken 1 Orr, Craig R. 1 Qin, Jing 1 Rabinowitz, Philip 1 Raff, Paul 1 Regev, Alon 1 Reidys, Christian Michael 1 Retakh, Vladimir Solomonovich 1 Reutenauer, Christophe 1 Richter, Nira 1 Saracino, Dan 1 Seidl, Martina 1 Shapiro, Louis W. 1 Shar, Nathaniel 1 Simpson, Jamie 1 Sloane, Neil James Alexander 1 Sontag, Eduardo D. 1 Stanley, Richard Peter 1 Stanton, Dennis W. 1 Sun, Xinyu 1 Werman, Michael 1 Wood, Philip Matchett 1 Zeilberger, Dominique 1 Zudilin, Wadim
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#### Serials

 21 Advances in Applied Mathematics 20 Journal of Difference Equations and Applications 18 Discrete Mathematics 14 The Electronic Journal of Combinatorics 11 American Mathematical Monthly 10 Annals of Combinatorics 8 Séminaire Lotharingien de Combinatoire 7 Journal of Mathematical Analysis and Applications 7 Journal of Combinatorial Theory. Series A 7 Journal of Symbolic Computation 6 SIAM Journal on Mathematical Analysis 6 Integers 5 The Mathematical Intelligencer 5 Proceedings of the American Mathematical Society 5 Proceedings of the National Academy of Sciences of the United States of America 3 Journal of Computational and Applied Mathematics 3 Transactions of the American Mathematical Society 3 European Journal of Combinatorics 3 The New York Journal of Mathematics 2 The Fibonacci Quarterly 2 Journal of the Australian Mathematical Society. Series A 2 Bulletin of the American Mathematical Society. New Series 2 Notices of the American Mathematical Society 2 Experimental Mathematics 1 Journal of Mathematical Biology 1 Journal of Statistical Physics 1 Mathematics of Computation 1 Mathematics Magazine 1 Acta Arithmetica 1 Advances in Mathematics 1 Algebra Universalis 1 American Journal of Mathematics 1 Ars Combinatoria 1 Inventiones Mathematicae 1 Journal of Differential Equations 1 Journal of Statistical Planning and Inference 1 Studies in Applied Mathematics 1 Theoretical Computer Science 1 Journal of Algorithms 1 Journal of the American Mathematical Society 1 SIAM Journal on Discrete Mathematics 1 International Journal of Computer Mathematics 1 Journal of Algebraic Combinatorics 1 Congressus Numerantium 1 ETNA. Electronic Transactions on Numerical Analysis 1 Electronic Research Announcements of the American Mathematical Society 1 The Ramanujan Journal 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 Journal of Integer Sequences 1 La Gaceta de la Real Sociedad Matemática Española 1 ACM Communications in Computer Algebra 1 Journal of Combinatorics and Number Theory 1 Journal of Combinatorics 1 Moscow Journal of Combinatorics and Number Theory 1 DML. Discrete Mathematics Letters
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#### Fields

 148 Combinatorics (05-XX) 47 Special functions (33-XX) 43 Number theory (11-XX) 32 Computer science (68-XX) 17 Difference and functional equations (39-XX) 13 Probability theory and stochastic processes (60-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 8 Functions of a complex variable (30-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 History and biography (01-XX) 7 Numerical analysis (65-XX) 6 Mathematical logic and foundations (03-XX) 5 General and overarching topics; collections (00-XX) 5 Statistical mechanics, structure of matter (82-XX) 3 Nonassociative rings and algebras (17-XX) 3 Partial differential equations (35-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Biology and other natural sciences (92-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Quantum theory (81-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Operations research, mathematical programming (90-XX)

#### Citations contained in zbMATH

181 Publications have been cited 1,943 times in 1,348 Documents Cited by Year
A holonomic systems approach to special functions identities. Zbl 0738.33001
Zeilberger, Doron
1990
The method of creative telescoping. Zbl 0738.33002
Zeilberger, Doron
1991
An algorithmic proof theory for hypergeometric (ordinary and “$$q$$”) multisum/integral identities. Zbl 0739.05007
Wilf, Herbert S.; Zeilberger, Doron
1992
A fast algorithm for proving terminating hypergeometric identities. Zbl 0701.05001
Zeilberger, Doron
1990
Proof of the alternating sign matrix conjecture. Zbl 0858.05023
Zeilberger, Doron
1996
A combinatorial proof of Bass’s evaluations of the Ihara-Selberg zeta function for graphs. Zbl 0921.05025
Foata, Dominique; Zeilberger, Doron
1999
Rational functions certify combinatorial identities. Zbl 0695.05004
Wilf, Herbert S.; Zeilberger, Doron
1990
Resurrecting the asymptotics of linear recurrences. Zbl 0579.05007
Wimp, Jet; Zeilberger, Doron
1985
Denert’s permutation statistic is indeed Euler-Mahonian. Zbl 0738.05001
Foata, Dominique; Zeilberger, Doron
1990
Random walk in a Weyl chamber. Zbl 0792.05148
Gessel, Ira M.; Zeilberger, Doron
1992
A proof of Andrews’ $$q$$-Dyson conjecture. Zbl 0565.33001
Zeilberger, Doron; Bressoud, David M.
1985
Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. Zbl 1108.05010
Apagodu, Moa; Zeilberger, Doron
2006
$$A=B$$. With foreword by Donald E. Knuth. Zbl 0848.05002
Petkovšek, Marko; Wilf, Herbert S.; Zeilberger, Doron
1996
The Goulden-Jackson cluster method: Extensions, applications and implementations. Zbl 0935.05003
Noonan, John; Zeilberger, Doron
1999
Proof of the refined alternating sign matrix conjecture. Zbl 0877.05004
Zeilberger, Doron
1996
The method of differentiating under the integral sign. Zbl 0717.33004
Almkvist, Gert; Zeilberger, Doron
1990
A combinatorial approach to matrix algebra. Zbl 0609.05008
Zeilberger, Doron
1985
A proof of Julian West’s conjecture that the number of two-stack-sortable permutations of length $$n$$ is $$2(3n)$$!/($$(n+1)$$!$$(2n+1)$$!). Zbl 0754.05006
Zeilberger, Doron
1992
Laguerre polynomials, weighted derangements, and positivity. Zbl 0662.05003
Foata, Dominique; Zeilberger, Doron
1988
Kathy O’Hara’s constructive proof of the unimodality of the Gaussian polynomials. Zbl 0726.05005
Zeilberger, Doron
1989
The enumeration of permutations with a prescribed number of “forbidden” patterns. Zbl 0974.05001
Noonan, John; Zeilberger, Doron
1996
Proof of Ira Gessel’s lattice path conjecture. Zbl 1203.05010
Kauers, Manuel; Koutschan, Christoph; Zeilberger, Doron
2009
Dodgon’s determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN. Zbl 0886.05002
Zeilberger, Doron
1997
Andre’s reflection proof generalized to the many-candidate ballot problem. Zbl 0508.05008
Zeilberger, Doron
1983
Refined restricted permutations. Zbl 1017.05014
Robertson, Aaron; Saracino, Dan; Zeilberger, Doron
2002
Proof of a conjecture of Chan, Robbins, and Yuen. Zbl 0941.05006
Zeilberger, Doron
1999
The quantum MacMahon master theorem. Zbl 1170.05012
Garoufalidis, Stavros; Lê, Thang T. Q.; Zeilberger, Doron
2006
Closed form (pun intended!). Zbl 0808.05010
Zeilberger, Doron
1993
Sister Celine’s technique and its generalizations. Zbl 0485.05003
Zeilberger, Doron
1982
Proof of George Andrews’s and David Robbins’s $$q$$-TSPP conjecture. Zbl 1255.05011
Koutschan, Christoph; Kauers, Manuel; Zeilberger, Doron
2011
A classic proof of a recurrence for a very classical sequence. Zbl 0883.05007
Foata, Dominique; Zeilberger, Doron
1997
Six etudes in generating functions. Zbl 0689.05003
Zeilberger, Doron
1989
A bijective proof of the Hook-length formula. Zbl 0498.68042
Franzblau, D. S.; Zeilberger, Doron
1982
A WZ proof of Ramanujan’s formula for $$\pi$$. Zbl 0849.33003
1994
A 2-coloring of $$[1, N]$$ can have $$(1/22) N^2+O(N)$$ monochromatic Schur triples, but not less. Zbl 0894.05052
Robertson, Aaron; Zeilberger, Doron
1998
Towards computerized proofs of identities. Zbl 0718.05010
Wilf, Herbert S.; Zeilberger, Doron
1990
A $$q$$-Foata proof of the $$q$$-Saalschütz identity. Zbl 0643.05003
Zeilberger, Doron
1987
Enumeration schemes and, more importantly, their automatic generation. Zbl 0931.05006
Zeilberger, Doron
1998
Hypergeometric series acceleration via the WZ method. Zbl 0884.05010
Amdeberhan, Tewodros; Zeilberger, Doron
1997
Reverend Charles to the aid of Major Percy and Fields Medalist Enrico. Zbl 0856.15007
Zeilberger, Doron
1996
Sharp upper bounds for the orders of the recurrences output by the Zeilberger and $$q$$-Zeilberger algorithms. Zbl 1121.33023
Mohammed, Mohamud; Zeilberger, Doron
2005
Determinants through the looking glass. Zbl 0994.05018
Amdeberhan, Tewodros; Zeilberger, Doron
2001
Permutation patterns and continued fractions. Zbl 0937.05004
Robertson, Aaron; Wilf, Herbert S.; Zeilberger, Doron
1999
Theorems for a price: tomorrow’s semi-rigorous mathematical culture. Zbl 1194.00058
Zeilberger, Doron
1993
Generalized Rogers-Ramanujan bijections. Zbl 0685.05003
Bressoud, David M.; Zeilberger, Doron
1989
A proof of the $$G_ 2$$ case of Macdonald’s root System-Dyson conjecture. Zbl 0643.05004
Zeilberger, Doron
1987
A short Hook-lengths bijection inspired by the Greene-Nijenhuis-Wilf proof. Zbl 0551.05010
Zeilberger, Doron
1984
Using the “Freshman’s dream” to prove combinatorial congruences. Zbl 1391.11047
Apagodu, Moa; Zeilberger, Doron
2017
The umbral transfer-matrix method. I: Foundations. Zbl 0961.05003
Zeilberger, Doron
2000
A pentagonal number sieve. Zbl 0910.05008
Corteel, Sylvie; Savage, Carla D.; Wilf, Herbert S.; Zeilberger, Doron
1998
Gauss’s $$_ 2F_ 1(1)$$ cannot be generalized to $$_ 2F_ 1(x)$$. Zbl 0764.33001
Zeilberger, Doron
1992
Rational function certification of multisum/integral/“q” identities. Zbl 0759.05007
Wilf, Herbert S.; Zeilberger, Doron
1992
A Stembridge-Stanton style elementary proof of the Habsieger-Kadell q- Morris identity. Zbl 0693.05009
Zeilberger, Doron
1990
A Markov chain occurring in enzyme kinetics. Zbl 0504.92019
Shapiro, Louis W.; Zeilberger, Doron
1982
A combinatorial proof of Dyson’s conjecture. Zbl 0492.05007
Zeilberger, Doron
1982
Explicit expressions for the expectation, variance and higher moments of the size of a $$(2n+1,2n+3)$$-core partition with distinct parts. Zbl 1375.05024
Zaleski, Anthony; Zeilberger, Doron
2017
Three-rowed CHOMP. Zbl 0977.91008
Zeilberger, Doron
2001
How to do MONTHLY problems with your computer. Zbl 0905.68082
Nemes, István; Petkovšek, Marko; Wilf, Herbert S.; Zeilberger, Doron
1997
A unified approach to Macdonald’s root-system conjectures. Zbl 0658.05005
Zeilberger, Doron
1988
The algebra of linear partial difference operators and its applications. Zbl 0458.39002
Zeilberger, Doron
1980
On the asymptotic statistics of the number of occurrences of multiple permutation patterns. Zbl 1312.05011
Janson, Svante; Nakamura, Brian; Zeilberger, Doron
2015
Formulæ for the number of partitions of $$n$$ into at most $$m$$ parts (using the quasi-polynomial ansatz). Zbl 1242.05020
Sills, Andrew V.; Zeilberger, Doron
2012
The Mahonian probability distribution on words is asymptotically normal. Zbl 1227.05009
Canfield, E. Rodney; Janson, Svante; Zeilberger, Doron
2011
On Frankel’s $$N$$-heap Wythoff’s conjectures. Zbl 1124.91016
Sun, Xinyu; Zeilberger, Doron
2004
Babson-Steingrímsson statistics are indeed Mahonian (and sometimes even Euler-Mahonian). Zbl 0994.05006
Foata, Dominique; Zeilberger, Doron
2001
A binomial coefficient identity associated to a conjecture of Beukers. Zbl 0885.05017
Ahlgren, Scott; Ekhad, Shalosh B.; Ono, Ken; Zeilberger, Doron
1998
Graphical major indices. Zbl 0856.05006
Foata, Dominique; Zeilberger, Doron
1996
On elementary methods in positivity theory. Zbl 0599.42500
Gillis, J.; Reznick, B.; Zeilberger, D.
1983
A short Rogers-Ramanujan bijection. Zbl 0476.05010
Bressoud, David M.; Zeilberger, Doron
1982
Uniqueness theorems for harmonic functions of exponential growth. Zbl 0319.31004
Zeilberger, Doron
1977
On the error in the numerical integration of Chebyshev polynomials. Zbl 0222.65029
Nicholson, D.; Rabinowitz, P.; Richter, N.; Zeilberger, D.
1971
The $$C$$-finite ansatz. Zbl 1268.05015
Zeilberger, Doron
2013
The quasi-holonomic ansatz and restricted lattice walks. Zbl 1193.05014
Kauers, Manuel; Zeilberger, Doron
2008
Self-avoiding walks, the language of science, and Fibonacci numbers. Zbl 0858.05004
Zeilberger, Doron
1996
The J. C. P. Miller recurrence for exponentiating a polynomial, and its $$q$$-analog. Zbl 0838.05006
Zeilberger, Doron
1995
Necessary conditions for distinct covering systems with square-free moduli. Zbl 0697.10004
Simpson, R. J.; Zeilberger, Doron
1991
A lattice walk approach to the ”inv” and ”maj” q-counting of multiset permutations. Zbl 0439.05004
Zeilberger, Doron
1980
Integrals involving Rudin-Shapiro polynomials and sketch of a proof of Saffari’s conjecture. Zbl 1391.11050
2017
Automated discovery and proof of congruence theorems for partial sums of combinatorial sequences. Zbl 1368.11020
Chen, William Y. C.; Hou, Qing-Hu; Zeilberger, Doron
2016
The holonomic ansatz. II: Automatic discovery(!) and proof(!!) of holonomic determinant evaluations. Zbl 1125.05009
Zeilberger, Doron
2007
Pythagorean primes and palindromic continued fractions. Zbl 1134.11322
Benjamin, Arthur T.; Zeilberger, Doron
2005
The number of solutions of $$X^ 2 = 0$$ in triangular matrices over $$GF(q)$$. Zbl 0851.15010
1996
A short proof of Jacobi’s formula for the number of representations of an integer as a sum of four squares. Zbl 0769.11020
Andrews, George E.; Ekhad, Shalosh B.; Zeilberger, Doron
1993
Multibasic Eulerian polynomials. Zbl 0790.05003
Foata, Dominique; Zeilberger, Doron
1991
A 21st century proof of Dougall’s hypergeometric sum identity. Zbl 0714.33002
1990
The Odlyzko conjecture and O’Hara’s unimodality proof. Zbl 0693.05008
Stanton, Dennis; Zeilberger, Doron
1989
Bijecting Euler’s partitions-recurrence. Zbl 0575.10007
Bressoud, David M.; Zeilberger, Doron
1985
Further properties of discrete analytic functions. Zbl 0359.30015
Zeilberger, Doron; Dym, Harry
1977
A case study in meta-automation: automatic generation of congruence automata for combinatorial sequences. Zbl 1358.68175
Rowland, Eric; Zeilberger, Doron
2014
How to generate as many Somos-like miracles as you wish. Zbl 1292.39004
2014
Rademacher’s infinite partial fraction conjecture is (almost certainly) false. Zbl 1301.11069
Sills, Andrew V.; Zeilberger, Doron
2013
A symbolic computation approach to a problem involving multivariate Poisson distributions. Zbl 1186.68587
Sontag, Eduardo D.; Zeilberger, Doron
2010
The holonomic ansatz. I: Foundations and applications to lattice path counting. Zbl 1125.05008
Zeilberger, Doron
2007
Disturbing the Dyson conjecture (in a GOOD way). Zbl 1121.05001
Sills, Andrew V.; Zeilberger, Doron
2006
Dave Robbins’ art of guessing. Zbl 1066.01516
Zeilberger, Doron
2005
The Markov-WZ method. Zbl 1072.33016
Mohammed, Mohamud; Zeilberger, Doron
2004
The collector’s brotherhood problem using the Newman-Shepp symbolic method. Zbl 1091.05004
Foata, Dominique; Zeilberger, Doron
2003
The umbral transfer-matrix method. V: The Goulden-Jackson cluster method for infinitely many mistakes. Zbl 0995.05013
Zeilberger, Doron
2002
There are more than $$2^{n/17}$$ $$n$$-letter ternary square-free words. Zbl 1018.68060
1998
$$q$$-Apéry irrationality proofs by $$q$$-WZ pairs. Zbl 0914.11042
Amdeberhan, Tewodros; Zeilberger, Doron
1998
Polynomial reduction and supercongruences. Zbl 07274358
Hou, Qing-Hu; Mu, Yan-Ping; Zeilberger, Doron
2021
D.H. Lehmer’s tridiagonal determinant: an étude in (Andrews-inspired) experimental mathematics. Zbl 1433.05031
2019
Using the “Freshman’s dream” to prove combinatorial congruences. Zbl 1391.11047
Apagodu, Moa; Zeilberger, Doron
2017
Explicit expressions for the expectation, variance and higher moments of the size of a $$(2n+1,2n+3)$$-core partition with distinct parts. Zbl 1375.05024
Zaleski, Anthony; Zeilberger, Doron
2017
Integrals involving Rudin-Shapiro polynomials and sketch of a proof of Saffari’s conjecture. Zbl 1391.11050
2017
Analysis of the gift exchange problem. Zbl 1430.05003
Apagodu, Moa; Applegate, David; Sloane, N. J. A.; Zeilberger, Doron
2017
Automated discovery and proof of congruence theorems for partial sums of combinatorial sequences. Zbl 1368.11020
Chen, William Y. C.; Hou, Qing-Hu; Zeilberger, Doron
2016
The (ordinary) generating functions enumerating $$123$$-avoiding words with $$r$$ occurrences of each of $$1, 2, \dots, n$$ are always algebraic. Zbl 1342.05007
Shar, Nathaniel; Zeilberger, Doron
2016
On the asymptotic statistics of the number of occurrences of multiple permutation patterns. Zbl 1312.05011
Janson, Svante; Nakamura, Brian; Zeilberger, Doron
2015
A case study in meta-automation: automatic generation of congruence automata for combinatorial sequences. Zbl 1358.68175
Rowland, Eric; Zeilberger, Doron
2014
How to generate as many Somos-like miracles as you wish. Zbl 1292.39004
2014
Generalizing and applying Michael Hirschhorn’s amazing algorithm to prove Ramanujan-type congruences. Zbl 1384.11107
Gnang, Edinah; Zeilberger, Doron
2014
A short proof of McDougall’s circle theorem. Zbl 1303.51006
Chamberland, Marc; Zeilberger, Doron
2014
The $$C$$-finite ansatz. Zbl 1268.05015
Zeilberger, Doron
2013
Rademacher’s infinite partial fraction conjecture is (almost certainly) false. Zbl 1301.11069
Sills, Andrew V.; Zeilberger, Doron
2013
Automatic generation of theorems and proofs on enumerating consecutive-Wilf classes. Zbl 1273.05007
Baxter, Andrew; Nakamura, Brian; Zeilberger, Doron
2013
The reciprocal of $$\sum_{n\geq 0}a^nb^n$$ for non-commuting $$a$$ and $$b$$, Catalan numbers and non-commutative quadratic equations. Zbl 1325.16032
2013
Zeroless arithmetic: representing integers ONLY using ONE. Zbl 1280.39001
Gnang, Edinah K.; Zeilberger, Doron
2013
Automatic counting of tilings of skinny plane regions. Zbl 1302.05032
2013
Balls in boxes: variations on a theme of Warren Ewens and Herbert Wilf. Zbl 1301.92073
2013
Using Noonan-Zeilberger functional equations to enumerate (in polynomial time!) generalized Wilf classes. Zbl 1259.05005
Nakamura, Brian; Zeilberger, Doron
2013
Formulæ for the number of partitions of $$n$$ into at most $$m$$ parts (using the quasi-polynomial ansatz). Zbl 1242.05020
Sills, Andrew V.; Zeilberger, Doron
2012
Corrigendum to “The Mahonian probability distribution on words is asymptotically normal”. Zbl 1242.05005
Canfield, E. Rodney; Janson, Svante; Zeilberger, Doron
2012
Toward a language theoretic proof of the four color theorem. Zbl 1237.05005
Cooper, Bobbe; Rowland, Eric; Zeilberger, Doron
2012
A new algorithm for proving global asymptotic stability of rational difference equations. Zbl 1266.39016
Hogan, Emilie; Zeilberger, Doron
2012
Proof of George Andrews’s and David Robbins’s $$q$$-TSPP conjecture. Zbl 1255.05011
Koutschan, Christoph; Kauers, Manuel; Zeilberger, Doron
2011
The Mahonian probability distribution on words is asymptotically normal. Zbl 1227.05009
Canfield, E. Rodney; Janson, Svante; Zeilberger, Doron
2011
The computational challenge of enumerating high-dimensional rook walks. Zbl 1234.05026
Kauers, Manuel; Zeilberger, Doron
2011
A symbolic computation approach to a problem involving multivariate Poisson distributions. Zbl 1186.68587
Sontag, Eduardo D.; Zeilberger, Doron
2010
Proof of Ira Gessel’s lattice path conjecture. Zbl 1203.05010
Kauers, Manuel; Koutschan, Christoph; Zeilberger, Doron
2009
The automatic central limit theorems generator (and much more!). Zbl 1210.05011
Zeilberger, Doron
2009
A symbolic finite-state approach for automated proving of theorems in combinatorial game theory. Zbl 1232.91071
Thanatipanonda, Thotsaporn “Aek”; Zeilberger, Doron
2009
A translation method for finding combinatorial bijections. Zbl 1229.05041
Wood, Philip Matchett; Zeilberger, Doron
2009
Commutation relations and Vandermonde determinants. Zbl 1168.15002
Bahturin, Yuri; Regev, Amitai; Zeilberger, Doron
2009
Efficient counting and asymptotics of $$k$$-noncrossing tangled diagrams. Zbl 1159.05027
Chen, William Y. C.; Qin, Jing; Reidys, Christian M.; Zeilberger, Doron
2009
The quasi-holonomic ansatz and restricted lattice walks. Zbl 1193.05014
Kauers, Manuel; Zeilberger, Doron
2008
Searching for strange hypergeometric identities by sheer brute force. Zbl 1210.33024
Apagodu, Moa; Zeilberger, Doron
2008
Experiments with a positivity-preserving operator. Zbl 1157.05003
Kauers, Manuel; Zeilberger, Doron
2008
Symbol-crunching with the gambler’s ruin problem. Zbl 1156.91007
Zeilberger, Doron
2008
Using Rota’s Umbral calculus to enumerate Stanley’s $$P$$-partitions. Zbl 1161.05005
2008
The holonomic ansatz. II: Automatic discovery(!) and proof(!!) of holonomic determinant evaluations. Zbl 1125.05009
Zeilberger, Doron
2007
The holonomic ansatz. I: Foundations and applications to lattice path counting. Zbl 1125.05008
Zeilberger, Doron
2007
An enquiry concerning human (and computer!) [mathematical] understanding. Zbl 1141.03002
Zeilberger, Doron
2007
Symbolic moment calculus. II: Why is Ramsey theory sooooo eeeenormously hard? Zbl 1124.05091
Zeilberger, Doron
2007
The number of [old-time] basketball games with final score $$n$$:$$n$$ where the home team was never losing but also never ahead by more than $$w$$ points. Zbl 1110.05006
Ayyer, Arvind; Zeilberger, Doron
2007
Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. Zbl 1108.05010
Apagodu, Moa; Zeilberger, Doron
2006
The quantum MacMahon master theorem. Zbl 1170.05012
Garoufalidis, Stavros; Lê, Thang T. Q.; Zeilberger, Doron
2006
Disturbing the Dyson conjecture (in a GOOD way). Zbl 1121.05001
Sills, Andrew V.; Zeilberger, Doron
2006
A fast algorithm for proving terminating hypergeometric identities. (Reprint). Zbl 1102.33017
Zeilberger, Doron
2006
Sharp upper bounds for the orders of the recurrences output by the Zeilberger and $$q$$-Zeilberger algorithms. Zbl 1121.33023
Mohammed, Mohamud; Zeilberger, Doron
2005
Pythagorean primes and palindromic continued fractions. Zbl 1134.11322
Benjamin, Arthur T.; Zeilberger, Doron
2005
Dave Robbins’ art of guessing. Zbl 1066.01516
Zeilberger, Doron
2005
On Frankel’s $$N$$-heap Wythoff’s conjectures. Zbl 1124.91016
Sun, Xinyu; Zeilberger, Doron
2004
The Markov-WZ method. Zbl 1072.33016
Mohammed, Mohamud; Zeilberger, Doron
2004
Chomp, recurrences and chaos(?). Zbl 1088.91011
Zeilberger, Doron
2004
Symbolic moment calculus. I: Foundations and permutation pattern statistics. Zbl 1053.05005
Zeilberger, Doron
2004
“Real” analysis is a degenerate case of discrete analysis. Zbl 1060.00003
Zeilberger, Doron
2004
The collector’s brotherhood problem using the Newman-Shepp symbolic method. Zbl 1091.05004
Foata, Dominique; Zeilberger, Doron
2003
Liebe Opa Paul, ich bin auch ein experimental scientist! Zbl 1081.00004
Zeilberger, Doron
2003
Computerized deconstruction. Zbl 1041.11052
Zeilberger, Doron
2003
Refined restricted permutations. Zbl 1017.05014
Robertson, Aaron; Saracino, Dan; Zeilberger, Doron
2002
The umbral transfer-matrix method. V: The Goulden-Jackson cluster method for infinitely many mistakes. Zbl 0995.05013
Zeilberger, Doron
2002
Determinants through the looking glass. Zbl 0994.05018
Amdeberhan, Tewodros; Zeilberger, Doron
2001
Three-rowed CHOMP. Zbl 0977.91008
Zeilberger, Doron
2001
Babson-Steingrímsson statistics are indeed Mahonian (and sometimes even Euler-Mahonian). Zbl 0994.05006
Foata, Dominique; Zeilberger, Doron
2001
The umbral transfer-matrix method. III: Counting animals. Zbl 0987.05009
Zeilberger, Doron
2001
The umbral transfer-matrix method. IV: Counting self-avoiding polygons and walks. Zbl 0969.05006
Zeilberger, Doron
2001
How Berger, Felzenbaum and Fraenkel revolutionized Covering Systems the same way that George Boole revolutionized Logic. Zbl 1004.11006
Zeilberger, Doron
2001
The umbral transfer-matrix method. I: Foundations. Zbl 0961.05003
Zeilberger, Doron
2000
The Goulden-Jackson cluster method for cyclic words. Zbl 0957.05011
Edlin, Anne E.; Zeilberger, Doron
2000
Symbol-crunching with the transfer-matrix method in order to count skinny physical creatures. Zbl 0954.82006
Zeilberger, Doron
2000
A combinatorial proof of Bass’s evaluations of the Ihara-Selberg zeta function for graphs. Zbl 0921.05025
Foata, Dominique; Zeilberger, Doron
1999
The Goulden-Jackson cluster method: Extensions, applications and implementations. Zbl 0935.05003
Noonan, John; Zeilberger, Doron
1999
Proof of a conjecture of Chan, Robbins, and Yuen. Zbl 0941.05006
Zeilberger, Doron
1999
Permutation patterns and continued fractions. Zbl 0937.05004
Robertson, Aaron; Wilf, Herbert S.; Zeilberger, Doron
1999
Automated counting of Lego towers. Zbl 0931.05022
Zeilberger, Doron
1999
A 2-coloring of $$[1, N]$$ can have $$(1/22) N^2+O(N)$$ monochromatic Schur triples, but not less. Zbl 0894.05052
Robertson, Aaron; Zeilberger, Doron
1998
Enumeration schemes and, more importantly, their automatic generation. Zbl 0931.05006
Zeilberger, Doron
1998
A pentagonal number sieve. Zbl 0910.05008
Corteel, Sylvie; Savage, Carla D.; Wilf, Herbert S.; Zeilberger, Doron
1998
A binomial coefficient identity associated to a conjecture of Beukers. Zbl 0885.05017
Ahlgren, Scott; Ekhad, Shalosh B.; Ono, Ken; Zeilberger, Doron
1998
There are more than $$2^{n/17}$$ $$n$$-letter ternary square-free words. Zbl 1018.68060
1998
$$q$$-Apéry irrationality proofs by $$q$$-WZ pairs. Zbl 0914.11042
Amdeberhan, Tewodros; Zeilberger, Doron
1998
Curing the Andrews syndrome. Zbl 0913.05005
1998
Dodgon’s determinant-evaluation rule proved by TWO-TIMING MEN and WOMEN. Zbl 0886.05002
Zeilberger, Doron
1997
A classic proof of a recurrence for a very classical sequence. Zbl 0883.05007
Foata, Dominique; Zeilberger, Doron
1997
Hypergeometric series acceleration via the WZ method. Zbl 0884.05010
Amdeberhan, Tewodros; Zeilberger, Doron
1997
How to do MONTHLY problems with your computer. Zbl 0905.68082
Nemes, István; Petkovšek, Marko; Wilf, Herbert S.; Zeilberger, Doron
1997
Proof of a conjecture on multisets of hook numbers. Zbl 0926.05004
Regev, Amitai; Zeilberger, Doron
1997
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van Poorten. Zbl 0895.11013
Krattenthaler, C.; Zeilberger, D.
1997
Proof of Conway’s lost cosmological theorem. Zbl 0883.05011
1997
The abstract lace expansion. Zbl 0882.05006
Zeilberger, Doron
1997
Proof of the alternating sign matrix conjecture. Zbl 0858.05023
Zeilberger, Doron
1996
$$A=B$$. With foreword by Donald E. Knuth. Zbl 0848.05002
Petkovšek, Marko; Wilf, Herbert S.; Zeilberger, Doron
1996
Proof of the refined alternating sign matrix conjecture. Zbl 0877.05004
Zeilberger, Doron
1996
The enumeration of permutations with a prescribed number of “forbidden” patterns. Zbl 0974.05001
Noonan, John; Zeilberger, Doron
1996
Reverend Charles to the aid of Major Percy and Fields Medalist Enrico. Zbl 0856.15007
Zeilberger, Doron
1996
Graphical major indices. Zbl 0856.05006
Foata, Dominique; Zeilberger, Doron
1996
Self-avoiding walks, the language of science, and Fibonacci numbers. Zbl 0858.05004
Zeilberger, Doron
1996
The number of solutions of $$X^ 2 = 0$$ in triangular matrices over $$GF(q)$$. Zbl 0851.15010
1996
The method of undetermined generalization and specialization. Zbl 0859.05022
Zeilberger, Doron
1996
...and 81 more Documents
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#### Cited by 1,376 Authors

 64 Zeilberger, Doron 35 Sato, Iwao 25 Chen, William Yong-Chuan 24 Guo, Victor J. W. 22 Garoufalidis, Stavros 21 Mansour, Toufik 20 Krattenthaler, Christian Friedrich 19 Zeng, Jiang 18 Kauers, Manuel 18 Schneider, Carsten 17 Koutschan, Christoph 16 Fischer, Ilse 15 Konvalinka, Matjaž 14 Mizuno, Hirobumi 13 Amdeberhan, Tewodros 13 Bousquet-Mélou, Mireille 13 Hou, Qinghu 12 Foata, Dominique C. 12 Pak, Igor 11 Chu, Wenchang 11 Ciucu, Mihai 11 Petkovšek, Marko 10 Corteel, Sylvie 9 Abramov, Sergeĭ Aleksandrovich 9 Guillera, Jesús 9 Liu, Jicai 9 Mishna, Marni 9 Moll, Victor Hugo 8 Bostan, Alin 8 Chen, Shaoshi 8 Gessel, Ira Martin 8 Han, Guo-Niu 8 Striker, Jessica 8 Sulanke, Robert A. 8 Xin, Guoce 8 Zudilin, Wadim 7 Apagodu, Moa 7 Bóna, Miklós 7 Bressoud, David M. 7 Brualdi, Richard Anthony 7 Ekhad, Shalosh B. (computer) 7 Elizalde, Sergi 7 Koepf, Wolfram A. 7 Melczer, Stephen 7 Mészáros, Karola 7 Mitsuhashi, Hideo 7 Raschel, Kilian 7 Salvy, Bruno 7 Thanatipanonda, Thotsaporn (Aek) 7 Vatter, Vincent Russell 6 Flajolet, Philippe 6 Konno, Norio 6 Le, Thang Tu Quoc 6 Morales, Alejandro H. 6 Mu, Yanping 6 Pillwein, Veronika 6 Rechnitzer, Andrew Daniel 6 Rinaldi, Simone 6 Sills, Andrew V. 6 Straub, Armin 6 Vignat, Christophe 6 Wang, Yi 6 Wilf, Herbert S. 5 Albert, Michael Henry 5 Behrend, Roger E. 5 Bouvel, Mathilde 5 Claesson, Anders 5 Colomo, Filippo 5 Fu, Shishuo 5 Morita, Hideaki 5 Prodinger, Helmut 5 Pronko, Andrei G. 5 Reidys, Christian Michael 5 Robertson, Aaron 5 Sagan, Bruce Eli 5 Shattuck, Mark A. 5 Stanton, Dennis W. 5 Sun, Brian Yi 5 Sun, Zhi-Wei 5 Takayama, Nobuki 5 Warnaar, S. Ole 5 White, Dennis E. 5 Williams, Lauren K. 5 Xia, Ernest X. W. 4 Andrews, George Eyre 4 Ayyer, Arvind 4 Banderier, Cyril 4 Blümlein, Johannes 4 Brignall, Robert 4 Defant, Colin 4 Deutsch, Emeric 4 Eu, Sen-Peng 4 Gerhold, Stefan 4 Guerrini, Veronica 4 Jin, Emma Yu 4 Kadell, Kevin W. J. 4 Kim, Jang Soo 4 Kitaev, Sergey 4 Kurkova, Irina A. 4 Loebl, Martin ...and 1,276 more Authors
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#### Cited in 225 Serials

 131 Advances in Applied Mathematics 114 Discrete Mathematics 103 Journal of Combinatorial Theory. Series A 55 Journal of Symbolic Computation 50 European Journal of Combinatorics 44 The Ramanujan Journal 38 Linear Algebra and its Applications 37 Journal of Difference Equations and Applications 35 Theoretical Computer Science 30 Advances in Mathematics 28 Annals of Combinatorics 26 Proceedings of the American Mathematical Society 23 Journal of Mathematical Analysis and Applications 22 Discrete Applied Mathematics 20 The Electronic Journal of Combinatorics 19 Journal of Computational and Applied Mathematics 16 Transactions of the American Mathematical Society 14 Journal of Number Theory 14 Journal of Algebraic Combinatorics 13 Rocky Mountain Journal of Mathematics 13 Mathematics of Computation 13 Journal of Algebra 13 Séminaire Lotharingien de Combinatoire 11 Journal of Statistical Planning and Inference 11 International Journal of Number Theory 9 Integers 8 Graphs and Combinatorics 7 Journal of Approximation Theory 7 Mathematische Annalen 7 Bulletin of the American Mathematical Society. New Series 6 Communications in Mathematical Physics 6 Israel Journal of Mathematics 6 Journal of Mathematical Physics 6 Proceedings of the National Academy of Sciences of the United States of America 5 Linear and Multilinear Algebra 5 Annales de l’Institut Fourier 5 Applied Mathematics and Computation 5 Algorithmica 5 SIAM Journal on Discrete Mathematics 5 Combinatorics, Probability and Computing 5 Journal of Integer Sequences 4 American Mathematical Monthly 4 Computers & Mathematics with Applications 4 Information Processing Letters 4 Journal of Statistical Physics 4 Letters in Mathematical Physics 4 Duke Mathematical Journal 4 Journal of Combinatorial Theory. Series B 4 Monatshefte für Mathematik 4 Results in Mathematics 4 Discrete & Computational Geometry 4 Numerical Algorithms 4 Indagationes Mathematicae. New Series 4 The Australasian Journal of Combinatorics 4 Experimental Mathematics 4 Journal de Théorie des Nombres de Bordeaux 4 Journal of Mathematical Sciences (New York) 4 Finite Fields and their Applications 4 Integral Transforms and Special Functions 4 Journal of High Energy Physics 4 Journal of Systems Science and Complexity 4 Journal of Statistical Mechanics: Theory and Experiment 4 Journal of Physics A: Mathematical and Theoretical 3 Communications in Algebra 3 Bulletin of Mathematical Biology 3 The Mathematical Intelligencer 3 The Annals of Probability 3 Inventiones Mathematicae 3 Journal of Computer and System Sciences 3 Journal of Functional Analysis 3 Journal of Pure and Applied Algebra 3 Programming and Computer Software 3 Studies in Applied Mathematics 3 International Journal of Algebra and Computation 3 Journal of Knot Theory and its Ramifications 3 Journal of Inequalities and Applications 3 Journal of the European Mathematical Society (JEMS) 3 Algebraic & Geometric Topology 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Quantum Information Processing 3 Mediterranean Journal of Mathematics 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Research in Number Theory 2 Artificial Intelligence 2 Journal d’Analyse Mathématique 2 Periodica Mathematica Hungarica 2 Chaos, Solitons and Fractals 2 Compositio Mathematica 2 Functiones et Approximatio. Commentarii Mathematici 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Applied Probability 2 Journal of Multivariate Analysis 2 Journal für die Reine und Angewandte Mathematik 2 Manuscripta Mathematica 2 Mathematische Zeitschrift 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Siberian Mathematical Journal 2 Order 2 Probability Theory and Related Fields 2 Information and Computation ...and 125 more Serials
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#### Cited in 58 Fields

 829 Combinatorics (05-XX) 301 Number theory (11-XX) 295 Special functions (33-XX) 160 Computer science (68-XX) 117 Linear and multilinear algebra; matrix theory (15-XX) 75 Probability theory and stochastic processes (60-XX) 54 Numerical analysis (65-XX) 53 Difference and functional equations (39-XX) 45 Group theory and generalizations (20-XX) 45 Statistical mechanics, structure of matter (82-XX) 40 Quantum theory (81-XX) 34 Functions of a complex variable (30-XX) 34 Convex and discrete geometry (52-XX) 30 Order, lattices, ordered algebraic structures (06-XX) 28 Approximations and expansions (41-XX) 26 Commutative algebra (13-XX) 26 Ordinary differential equations (34-XX) 25 Algebraic geometry (14-XX) 25 Manifolds and cell complexes (57-XX) 24 Associative rings and algebras (16-XX) 24 Nonassociative rings and algebras (17-XX) 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Dynamical systems and ergodic theory (37-XX) 19 Field theory and polynomials (12-XX) 18 Biology and other natural sciences (92-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 14 Partial differential equations (35-XX) 13 Real functions (26-XX) 11 Topological groups, Lie groups (22-XX) 11 Statistics (62-XX) 8 General and overarching topics; collections (00-XX) 8 Potential theory (31-XX) 8 Sequences, series, summability (40-XX) 8 Information and communication theory, circuits (94-XX) 7 History and biography (01-XX) 7 Integral transforms, operational calculus (44-XX) 6 Several complex variables and analytic spaces (32-XX) 6 Operator theory (47-XX) 5 Operations research, mathematical programming (90-XX) 5 Systems theory; control (93-XX) 4 Measure and integration (28-XX) 4 Functional analysis (46-XX) 4 Geometry (51-XX) 4 Differential geometry (53-XX) 4 Algebraic topology (55-XX) 3 Category theory; homological algebra (18-XX) 2 Mathematical logic and foundations (03-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral equations (45-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Mechanics of particles and systems (70-XX) 2 Fluid mechanics (76-XX) 2 Mathematics education (97-XX) 1 General algebraic systems (08-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX)

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