Last Update: Aug. 8, 2008
Here are most of my articles that were also published
elsewhere. The Articles that were written after 1990 come
with a "front" .html file, and are preprints. Those
that were written prior to 1990 are .pdf files of scans
of the published articles, kindly prepared by the
brilliant young combinatorialist, Larry X. W. Wang,
from Nankai University, who during my Nov. 2007 visit to Bill Chen's
Combinatorics Kingdom, presented me with a beautifully prepared
CD with most of my published articles.
Be sure to also look at
The Personal Journal of Shalosh B. Ekhad and
Doron Zeilberger, that contains papers
that are exlusively published in this website.
Here is my
CV, that includes the list of publications. (last update: Jan. 25, 2008).
Proof of Ira Gessel's Lattice Path Conjecture By Manuel Kauers, Christoph Koutschan, and Doron Zeilberger
Commutation Relations and Vandermonde Determinants by Yuri Bahturin, Amitai Regev, and Doron Zeilberger
Efficient Counting and Asymptotics of k-noncrossing Tangled Diagrams by William Y.C. Chen, Jing Qin, Christian M. Reidys and Doron Zeilberger
Experiments with a Positivity-Preserving Operator by Manuel Kauers and Doron Zeilberger [To Appear in Experimental Mathematics]
The Quasi-Holonomic Ansatz and Restricted Lattice Walks by Manuel Kauers and Doron Zeilberger [To appear in J. of Difference Equations and Applications, special issue in honor of Gerry Ladas' 70th Birthday]
A Translation Method for Finding Combinatorial Bijections by Philip Matchett Wood and Doron Zeilberger. [To appear in Annals of Combinatorics]
Enumerative and Algebraic Combinatorics By Doron Zeilberger. [To Appear in "Princeton Companion to Mathematics", Princeton University Press, edited by Tim Gowers].
Searching For Strange Hypergeometric Identities By Sheer Brute Force by Moa Apagodu and Doron Zeilberger. [Appeared in INTEGERS, 8(2008), A36.]
Using Rota's Umbral Calculus to Enumerate Stanley's P-Partitions by Doron Zeilberger. [Appeared in Adv. Applied Mathematics v. 41 (2008), 206-217.]
Two Dimensional Directed Lattice Walks with Boundaries by Arvind Ayyer and Doron Zeilberger. [Appeared in "Tapas in Experimental Mathematics", Contemporary Mathematics, v. 457 (2008), 1-20, (Tewodros Amdeberhan and Victor Moll, eds.)].
Symbol Crunching with the Gambler's Ruin Problem by Doron Zeilberger. [Appeared in "Tapas in Experimental Mathematics", Contemporary Mathematics, v. 457 (2008), 285-292, (Tewodros Amdeberhan and Victor Moll, eds.)].
An Enquiry Concerning Human (and Computer!) [Mathematical] Understanding by Doron Zeilberger. [Appeared in: C.S. Calude ,ed., "Randomness & Complexity, from Leibniz to Chaitin", World Scientific, Singapore, Oct. 2007.]
FIVE Applications of Wilf-Zeilberger Theory to Enumeration and Combinatorics by Moa Apagodu and Doron Zeilberger. [Appeared in "COMPUTER ALGEBRA 2006, Latest Advances in Symbolic Algorithms" [Abramov Festschrift, dedicated to Sergey Abramov's 60th birthday], edited by Ilias S Kotsireas and Eugene V Zima, World Scientific, Aug. 2007.]
The HOLONOMIC ANSATZ I. Foundations and Applications to Lattice Path Counting by Doron Zeilberger. [Appeared in Annals of Combinatorics 11(2007) 227-239].
The HOLONOMIC ANSATZ II. Automatic DISCOVERY(!) and PROOF(!!) of Holonomic Determinant Evaluations by Doron Zeilberger [Appeared in Annals of Combinatorics 11(2007) 241-247].
"Trivializing" Generalizations of Some Izergin-Korepin-Type Determinants by Tewodros Amdeberhan and Doron Zeilberger. [Appeared in Discrete Mathematics and Theoretical Computer Science 9 (2007), 203-206 .]
Symbolic Moment Calculus II.: Why is Ramsey Theory Sooooo Eeeenormoulsy Hard? by Doron Zeilberger. [Appeared in "Combinatorial Number Theory", B. Landman et. al, editors, in Celebration of the 70th Birthday of Ronald Graham, de Gruyter, 2007. (Co-publised in INTEGERS, 7(2)(2007), A34.]
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 by Arvind Ayyer and Doron Zeilberger. [Appeared in Electronic J. of Combinatorics 14(1) (2007), R19 [8 pp]]
A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture by Shalosh B. Ekhad, Vince Vatter and Doron Zeilberger . [Appeared in the Personal Journal of Ekhad and Zeilberger and Vince Vatter's website].
Multi-Variable Zeilberger and Almkvist-Zeilberger Algorithms and the Sharpening of Wilf-Zeilberger Theory By Moa Apagodu (formerly Mohamud Mohammed) and Doron Zeilberger. [Appeared in Adv. Appl. Math. 37(2006)(Special Regev issue), 139-152].
Disturbing the Dyson Conjecture (in a GOOD Way) by Andrew V. Sills and Doron Zeilberger. [Appeared in Experimental Mathematics 15(2006), 187-191.]
Pythagorean Primes and Palindromic Continued Fractions By Arthur T. Benjamin and Doron Zeilberger. [Appeared in INTEGERS 5(1) (2005) A30]
DECONSTRUCTING the ZEILBERGER algorithm by Doron Zeilberger . [Appeared in J. of Difference Equations and Applications 11(2005), 851-856.]
Dave Robbins's Art of Guessing By Doron Zeilberger. [Appeared in Adv. Appl. Math. 34(2005), 939-954.]
Sharp Upper Bounds for the Orders of the Recurrences Outputted by the Zeilberger and q-Zeilberger Algorithms By Mohamud Mohammed and Doron Zeilberger. [Appeared in J. Symbolic Computation 39(2005), 201-207.]
Chomp, Recurrences, and Chaos By Doron Zeilberger. [Appeared in J. Difference Equations and its Applications 10(2004), 1281-1293. (special issue in honor of Saber Elaydi)].
Symbolic Moment Calculus I.: Foundations and Permutation Pattern Statistics By Doron Zeilberger. [Appeared in Annals of Combinatorics 8(2004), 369-378.]
The Markov-WZ Method By Mohamud Mohammed and Doron Zeilberger. [Appeared in Elec J. Combinatorics 11(2004), R53.]
On Fraenkel's N-Heap Wythoff Conjecture By Xinyu Sun and Doron Zeilberger. [Appeared in Annals of Combinatorics 8(2004) 225-238.]
"Real" Analysis is a Degenerate Case of Discrete Analysis By Doron Zeilberger. [Appeared in the book "New Progress in Difference Equations"(Proc. ICDEA 2001), edited by Bernd Aulbach, Saber Elaydi, and Gerry Ladas, and publisher by Taylor & Francis, London, 2004.]
The Collector's Brotherhood Problem Using the Newman-Shepp Symbolic Method By Dominique Foata and Doron Zeilberger. [Appeared in Algebra Universalis (special Rota memorial issue) 49 (2003), 387-395.]
Lieber Opa Paul, Ich Bin Auch Ein Experimental Scientist By Doron Zeilberger. [Appeared in Adv. Appl. Math. v. 30 (2003), 633-654.]
Computerized Deconstruction By Doron Zeilberger, [Appeared in Adv. Appl. Math. v. 31 (2003), 532-543.]
A WZ Proof of a "Curious" Identity by Shalosh B. Ekhad and Mohamud Mohammed, [Appeared in INTEGERS 3 (2003), A6.]
The Umbral Transfer-Matrix Method. V. The Goulden-Jackson Cluster Method for Infinitely Many Mistakes By Doron Zeilberger. [ Appeared in INTEGERS, v. 2 (2002), A5) ]
Determinants Through The Looking Glass By Tewodros Amdeberhan and Doron Zeilberger. [Appeared in Adv. Appl. Math. v. 27 (2001) Aug/Oct. Numbers 2/3 (FoataFest Special double issue), 225-230].
Babson-Steingrimsson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian) By Dominique Foata and Doron Zeilberger. [Appeared in Adv. Appl. Math. v. 27 (2001) Aug/Oct. Numbers 2/3 (FoataFest Special double issue), 390-404].
The Umbral Transfer-Matrix Method. III. Counting Animals By Doron Zeilberger (Appeared in New York J of Mathematics 7(2001), 223-231.
How Berger, Felzenbaum, and Fraenkel Revolutionized COVERING SYSTEMS The Same Way that George Boole Revolutionized LOGIC By Doron Zeilberger. [Appeared in Elect. J. Combinatorics 8(2) (2001) (special issue in honor of Aviezri Fraenkel), A1]
The Umbral Transfer-Matrix Method. IV. Counting Self-Avoiding Polygons and Walks By Doron Zeilberger. [Appeard in Elec. J. Comb. 8(1)(2001), R28].
Three-Rowed CHOMP By Doron Zeilberger. [Appeared in Adv. Appl. Math. v. 26 (2001), 168-179].
The Goulden-Jacskon Cluster Method For Cyclic Words By Anne E. Edlin and Doron Zeilberger. (Advances in Applied Mathematics v. 25 (2000), 228-232.)
Symbol-Crunching with the Transfer-Matrix Method in Order to Count Skinny Physical Creatures By Doron Zeilberger. ( INTEGERS, v. 0 (2000), A9) .
Permutation Patterns and Continued Fractions By Aaron Robertson, Herb Wilf, and Doron Zeilberger. (Appeared in Elec. J. Combinatorics 6 (1999), R38.)
Automated Counting of LEGO Towers. By Doron Zeilberger. (Appeared in J. Difference Eq. Appl. 5 (1999), 323-333).
`The Goulden-Jackson Cluster Method: Extensions, Applications, and Implementations' By John Noonan and Doron Zeilberger. (Appeared in J. Difference Eq. Appl. 5 (1999), 355-377).
PLANE GEOMETRY: An Elementary School Textbook (ca. 2050) By Shalosh B. Ekhad, XIV, downloaded from the future by Doron Zeilberger. (Appeared in Mathematical Intelligencer 21(3) (Summer 1999), 64-70)
Combinatorial Proofs of Bass's Evaluations of the Ihara-Selberg Zeta function of a Graph By Dominique Foata and Doron Zeilberger. (Appeared in Trans. Amer. Math. Soc. 351 (1999), 2257--2274 .)
There Are More Than 2**(n/17) n-Lettered Ternanry Square-Free Words By Shalosh B. Ekhad and Doron Zeilberger. (J. Integer Sequences (electronic), 98.1.9)
Curing the Andrews Syndrome By Shalosh B. Ekhad and Doron Zeilberger. (J. of Difference Equations and Applications 4(1998), 299-310)
`A 2-Coloring of [1,N] Can Have (1/22)N^2+O(N) Monochromatic Schur Triples, But Not Less!' By Aaron Robertson and Doron Zeilberger. Electronic Journal of Combinatorics 5(1998), R19.
q-Apery Irrationality Proofs by q-WZ Pairs By Tewodros Amdeberhan and Doron Zeilberger. (Adv. Appl. Math. 20 (1998), 275-283.)
A Binomial Coefficient Identity Associated to a Conjecture of Beukers, by Scott Ahlgren, Shalosh B. Ekhad, Ken Ono, and Doron Zeilberger. Electronic Journal of Combinatorics 5(1998), R10.
How Much Should a Nineteenth-Century French Bastard Inherit. by Doron Zeilberger (J. Difference Eq. Appl. 3(1998), 385-388. (Special issue in honor of Gerry Ladas.)
A pentagonal number sieve by Sylvie Corteel, Carla Savage, Herbert Wilf and Doron Zeilberger (J. Comb. Theory (Ser.A) 82(1998), 186-192.)
A classic proof of a recurrence for a very classical sequence By Dominique Foata and Doron Zeilberger. (J. Comb. Theor.-Ser. A., 80(1997), 380-384)
Math Bite: Proof of an Empirical Observation Made by Amos Oz's character by Doron Zeilberger(Math. Magazine 70 No. 4 (Oct. 1997), 291)
`Proof of a Determinant Evaluation Conjectured by Bombieri, Hunt, and van der Poorten' By Christian Krattenthaler and Doron Zeilberger. (New York J. of Math. (Electronic), 3(1997), 54-102.)
The Abstract Lace Expansion By Doron Zeilberger. Adv. Appl. Math. 19(1997), 355-359.
`Proof of Conway's Lost Cosmological Theorem' By Shalosh B. Ekhad and Doron Zeilberger (Elect. Res. Announcements of the AMS 3(1997), 78-82.)
A Condensed Condensation Proof of Determinant Evaluation Conjectured by Greg Kuperberg and Jim Propp. By Tewodros Amdeberhan and Shalosh B. Ekhad. [J. Comb. Theory (series A) 78(1997), 169-170.]
A comparison of two methods for random labellings of balls by vectors of integers by Doron Zeilberger (Appeared in Advances in Combinatorial Methods and Applications to Probability and Statistics, N. Balakrishnan, ed., Birkhauser, 1997 (Mohanty Festschrift).)
Dodgson's Determinant-Evaluation Rule Proved by TWO-TIMING MEN and WOMEN. by Doron Zeilberger (Appeared in the Elect. J. of Combinatorics 4(2)(1997), [Wilf Festschrift volume], R22.)
Hypergeometric Series Acceleration via the WZ method By Tewodros Amdeberhan and Doron Zeilberger. (Appear in the Elect. J. of Combinatorics 4(2) (1997), [Wilf Festschrift volume].), R3
A Condensed Condensation Proof of Determinant Evaluation Conjectured by Greg Kuperberg and Jim Propp. by Tewodros Amdeberhan, and Shalosh B. Ekhad [Appeared in J. Comb. Theory (series A) 78(1997) 169-170].
Self-Avoiding Walks, the language of science, and Fibonacci numbers by Doron Zeilberger (Appeared in J. Stat. Planning and Inference 54(1996), 135-138)
Reverend Charles to the aid of Major Percy and Fields-medalist Enrico by Doron Zeilberger (Appeared in the June 1996(103,no.6) issue of Amer. Math. Monthly, 501-502)
Proof of the refined alternating sign matrix conjecture by Doron Zeilberger (Appeared in New York J. of Mathematics, v. 2 (1996), 59-68)
``The graphical major index'' by Dominique Foata and Doron Zeilberger (appeared in J. Comput. Applied Math (special issue on q-series) 68(1996) 79-101.
The method of undetermined generalization and specialization illustrated with Fred Galvin's amazing proof of the Dinitz conjecture by Doron Zeilberger (Appeared in the Amer. Math. Monthly, March 1996 (103, no. 3), 233-239)
A generalization of a curiosity that Feynman remembered all his life by Bill Beyer, Jim Louck and Doron Zeilberger (Appeared as a Math Bite in Math. Magazine, March 1996)
If A_n has 6n dyes in a box, with which he has to fling at least n sixes, then A_n has an easier task than A_{n+1}, at Eaven Luck by Doron Zeilberger (Appeared as a filler in the AMM, March 1996)
A short computer-generated proof of Abel's identity , by S. B. Ekhad and John Majewicz. [Appeared in Elect. J. Combi. 3(2) (1996)[Foata issue], R16.]
Proof of the alternating sign matrix conjecture(Elec. J. Comb. 3(2)(1996), R13) by Doron Zeilberger
An explicit formula for the number of solutions of X^2=0 in triangular matrices over GF(q) (Elec. J. Comb. 3(1996), R2 ) by Shalosh B. Ekhad and Doron Zeilberger
A short computer-generated proof of Abel's identity by Shalsoh B. Ekhad and John Majewicz (Appeared in Elect. J. Combi. 3(2) (1996)[Foata issue], R16.)
Three recitations on holonomic functions and hypergeometric series by Doron Zeilberger ( Originally appeard in the (Elec.) proceedings of the Seminaire Lotharingine v.24, this revised, updated version, appeared in J. Symbolic Comp 20(1995), 699-724.
A short (formal calculus) proof of the Bieberbach conjecture (after L. Weinstein) by Shalosh B. Ekhad and Doron Zeilberger. (Appeard in `Jerusalem Combinatorcs' Proc. 1993, H. Barcello and G. Kalai, eds., Contemporary Math 178 (1995), 113-115)
The J.C.P. Miller Recurrence for exponentiating a polynomial, and its q-Analog by Doron Zeilberger (Appeard in J. Difference Eqs. and Appls. 1(1995), 57-60
Chu's 1303 identity implies Bombieri's 1990 inequality by Doron Zeilberger [appeard in the Amer. Math. Monthly 101(1994) 894-896 ]
A computer algebra approach to the discrete Dirichlet problem by Craig Orr and Doron Zeilberger (Appeared in J. Symbolic Computation 18(1994), 87-90.
Two EZ proofs of sin^2 z+ cos^2 z=1 by Leon Ehrenpreis and Doron Zeilberger (Appeard as a filler in Amer. Math. Monthly 101(1994), p. 691).
Combinatorial Proofs of Capelli and Turnbull's identities from classical invariant theory by Dominique Foata and Doron Zeilberger (Appeard in Elec. J. Comb. 1(1994), R1.
A constant term identity featuring the ubiquitous (and mysterious) Andrews-Mills-Robbins-Rumsey numbers1,2,7,42,429, ... by Doron Zeilberger (Appeard in J. Combinatorial Theory (ser. A) 66 (1994), 17-27.)
Talmudic lattice path counting by Jane Friedman, Ira Gessel and Doron Zeilberger (Appeard in J. Combinatorial Theory (ser. A) 68 (1994), 215-217.)
Proof of q-analog of a constant term identity conjectured by Forrester by Doron Zeilberger (Appeard in J. Combinatorial Theory (ser. A) 66 (1994), 311-312.)
Towards a WZ proof of Mehta's integral by Doron Zeilberger (Appeard in SIAM J. Math. Anal. 25 (1994) [Askey issue], 812-814.)
On an identity of Daubechies by Doron Zeilberger (Appeard in the Amer. Math. Monthly 100(1993), 487.)
A short proof of Jacobi's formula for the number of representations of an integer as a sum of four squares by George Andrews, Shalosh B. Ekhad, and Doron Zeilberger) (Appeared in Amer. Math. Monthly 100(1993), 274-276.)
CLOSED FORM (pun intended!) by Doron Zeilberger (Appeared in Contemporary Math. 143 (1993), 579-608.)
Gert Almkvist's generalization of a mistake of Bourbaki by Doron Zeilberger, (Appeared Contemporary Mathematics 143 (1993), 609-612.)
Identities in search of identity by Doron Zeilberger, (Appeared in J. Theoretical Computer Science, 117 (1993), 23-38.)
A generalization of Odlyzko's conjecture: the coefficients of $(1-q)^{j} /(( 1- q^{2n} ) ... (1- q^{2n+2j} ))$ alternate in sign by Jane Friedman and Doron Zeilberger, (Appeared in Proc. Amer. Math. Soc. 118, 1013 (1993).)
A proof of Julian West's conjecture that the number of 2-stack-sortable permutations of length n is} 2 (3n)! /((2n+1)! (n+1)!) By Doron Zeilberger. (Appeared in: Discrete Math. 102 (1992), 85-93 .)
Random Walk in a Weyl chamber By Ira Gessel and Doron Zeilberger. (Appeared in Proc. Amer. Math. Soc. 115 (1992), 27-31.
Gauss's 2F1(1) cannot be generalized to 2F1(x), By Doron Zeilberger. (Appeared in J. Comp. Appl. Math. 39 (1992) 379-382 .