Last update: April 6, 2008
All the papers here are exclusively published here, unless
noted otherwise.
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AsyRec: A Maple package for Computing the
Asymptotics of Solutions of Linear Recurrence Equations
with Polynomial Coefficients
by Doron Zeilberger (Written: April 6, 2008).
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Four Solutions to David Beckwith's
American Mathematical Monthly Problem 11343 (Feb. 2008)
Compiled by Doron Zeilberger (Written: Feb. 8, 2008).
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How Likely is Polya's Drunkard to Return to the Pub Without Getting Mugged?
(In d-Dimensional Manhattan)
by Doron Zeilberger (Written: Dec. 18, 2007).
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The Number of Ways of Walking in
x1 ≥ ... ≥ xk ≥ 0
for n Days, Starting and Ending at the Origin,
Where at each Day you may either Stay in Place
or Move One Unit in any Direction,
Equals the Number of
n-Cell Standard Young Tableaux with ≤ 2k+1 Rows.
by Doron Zeilberger (Written: Dec. 6, 2007).
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by Doron Zeilberger (Written: June 15, 2007).
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Proof of a Conjecture of Philippe Di Francesco and Paul Zinn-Justin
related to the qKZ equations and to
Dave Robbins' Two Favorite Combinatorial Objects
by Doron Zeilberger (Written: March 20, 2007).
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Martin KRUSKAL(Sept. 28, 1925-Dec.26, 2006) and
Peter HAMMER(Dec. 23, 1936-Dec. 27, 2006), TWO GIANTS OF DISCRETE MATHEMATICS
by Doron Zeilberger (Written: Dec. 29, 2006).
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On Vince Vatter's Brilliant Extension of Doron Zeilberger's
Enumeration Schemes for Counting Herb Wilf's Classes
by Doron Zeilberger (Written: Dec. 29, 2006).
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In How Many Ways Can n (Straight) Men and n (Straight) Women Get Married,
if Each Person Has Exactly k Spouses
by Shalosh B. Ekhad and Doron Zeilberger (Written: Dec. 29, 2006,
Revised: Jan. 11, 2007).
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Proof of a Conjecture of Amitai
Regev about Three-Rowed Young Tableaux
(and much more!) by Shalosh B. Ekhad and Doron Zeilberger.
(Written: Dec. 8, 2006).
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Fully AUTOMATED Computerized Redux of Feller's (v.1) Ch. III (and Much More!)
by Doron Zeilberger (Written: Nov. 14, 2006).
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A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture
by Shalosh B. Ekhad, Vince Vatter and Doron Zeilberger .
[ co-published in
Vince Vatter's website and the arxiv.org.]
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What Is Experimental Mathematics?
by Doron Zeilberger
(Written: April 4, 2006).
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Proof of the Celebrated Goldbach's Theorem
by Doron Zeilberger
(Written: April 1, 2006).
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Automatc CountTilings
by Doron Zeilberger
(Written: Jan. 20, 2006)
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How to Play Backgammon (if you must) and how to Research it (if you have
time)
by Shalosh B. Ekhad and Doron Zeilberger
(Written: Nov. 15, 2005).
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An Umbral Approach to the Hankel Trasform for Sequences
by Doron Zeilberger
(Written: Nov. 7, 2005).
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Another Proof that Euler Missed: Jonas Sjöstrand's Amazingly
Simple (and Lovely!) Proof of the No-Longer-So-Amazing Loehr-Warrington
Lattice Paths Conjecture
by Doron Zeilberger
(Written: Oct. 23, 2005).
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A Snappy Proof That 123-Avoiding Words are Equinumerous With 132-Avoiding
Words
by
Doron Zeilberger
(Written: April 11, 2005).
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A Perfect Rhythmic Tilings of QUADRUPLETS
by
Shalosh B. Ekhad and Lara Pudwell
(Written: Nov. 30, 2004).
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Book Review of J. Borwein and D. Bailey's Mathematic by Experiments and
J. Borwein, D. Bailey and R. Girgensohn's Experimentation in Mathematics
Reviewed by
Doron Zeilberger (Written: Nov. 12, 2004).
[Also appeared in American Scientist, March-April 2005 issue].
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How Adam Marcus and Gabor Tardos Divided and Conquered the Stanley-Wilf
Conjecture (An Étude in Paramathematics)
by
Doron Zeilberger (Written: Oct. 20, 2004).
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A 360-Character Maple Code that Proves (in 0.05 Seconds!) Sergey Sadov's
Ptolemy-type Theorem that
if ABCD are four Points on a Circle (arranged clockwise) then
|AB|.|BC|.|CA|+|AC|.|CD|.|DA|
=|BC|.|CD|.|DB|+|AB|.|BD|.|DA|
by Shalosh B. Ekhad (Written: Oct. 14, 2004).
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Forty "Strange" Computer-Discovered [and Computer-Proved!] Hypergeometric
Series Evaluations.
by
Shalosh B. Ekhad (Written: Oct. 12, 2004).
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A Fibonacci-Counting Proof Begged by Benjamin and Quinn
by
Doron Zeilberger (Written: May 24, 2004).
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A Loving Rendition of the Marcus-Tardos Amazing Proof of the
Füredi-Hajnal Conjecture
by
Doron Zeilberger (Written: Nov. 30, 2003).
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All the Moments of the Vertex Degrees of Randomly Generated Graphs
by
Doron Zeilberger (Written: Nov. 30, 2003).
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Review of George Szpiro's `Kepler's Conjecture'
by
Doron Zeilberger (published in Science, Aug. 29, 2003).
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Towards a SymbolicComputational Philosophy (and Methodology!) for
Mathematics
by Doron Zeilberger. (Written: Dec. 12, 2002).
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I Am Sorry, Richard Ehrenborg and Margie Readdy, About Your Two Conjectures,
But One is FAMOUS, While The Other Is FALSE
by
Doron Zeilberger (Written: July 2, 2002).
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How Many Singles, Doubles, Triples, Etc. Should The Coupon
Collector Expect
by
Doron Zeilberger (Written: July 5, 2001).
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R(n,n) IS LESS THAN A CONSTANT TIMES (3.9999999999999997)**n
by Shalosh B. Ekhad and
Doron Zeilberger (Written: April 1, 2001!).
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The Umbral Transfer Matrix Method: II. Counting Plane Partitions
by Doron Zeilberger (Written: Oct. 26, 2000) .
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Remarks On The PARRONDO PARADOX
by Shalosh B. Ekhad and Doron Zeilberger (Written: Oct. 13, 2000) .
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Proof of an Identity
Conjectured by Iossif Polterovitch that
Came Up in the Agmon-Kannai Asymptotic Theory of the Heat Kernel
by Doron Zeilberger (Written: Aug. 11, 2000) .
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Review of Dave Bressoud's "Proofs and Confirmations: The
Story of the Alternating Sign Matrix Conjecture"
by Doron Zeilberger (Written: April 12, 2000) .
(Also appeared in the Amer. Math. Monthly, Feb. 2001 issue)
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RODICA SIMION (1955-2000): An (almost) Perfect Enumerator
and Huamn Being
by Doron Zeilberger (Written: Jan. 12, 2000) .
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Does Dreidel Last O(NUTS**2) Spins?
by Doron Zeilberger (Written: Kislev 30, 5760) .
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The Revenge of the Plain Mathematician: How I Answered Two Questions
by Two Fancy Jerusalem Mathematicians In One Day
by Doron Zeilberger (Written: Oct. 5, 1999.) .
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The Mathematics Behind the Proposed Reform of the Hebrew Calendar
by Doron Zeilberger ( released April 1, 1999!).
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Mordukh Primak: The Man Who Really Loved Optimization
by Doron Zeilberger. (Also appeared in Temple University
Math Monthly (TUMM), v.2 (1999), Issue 5, 24 Feb. 1999 .)
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A User's Manual for RORTY: A Maple Package for Finding the Final
Vocabularies of Texts.
by Shalosh B. Ekhad and Doron Zeilberger.
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Some Stretching, Squeezing and Folding Caused By John Allen Paulos's
Masterpiece `Once Upon a Number'.
by Doron Zeilberger.
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WZ Theory, Chapter II
by Doron Zeilberger.
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Sylvie Corteel's One-Line Proof of a Partition Theorem
Generated by Andrews-Paule-Riese's Computer
Reported by Doron Zeilberger.
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A 2-Minute Proof of the 2nd-Most Important Theorem of the
2nd Millenium
By Doron Zeilberger.
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The Generalized U2-Flashlight Microsoft 5-Minute Puzzle
By Shalosh B. Ekhad and Doron Zeilberger.
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The Combinatorial Astrology of Rabbi Abraham Ibn Ezra
By Doron Zeilberger.
(A Spanish translation appeared in
"La Gaceta"(of the Spanish Royal Mathematical
Society), Vol. 1, no. 3, Sep-Dec. (1998) 382-385)
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``A Heterosexual Mehler Formula for the Straight Hermite Polynomials
(A La Foata)''
By
Doron Zeilberger.
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Aufgabe VII.47 of Polya-Szego Immediately Implies Dave Robbins's
Multi-Integral Evaluation
By Doron Zeilberger
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Mathematical Genitalysis: A Powerful New Combinatorial Theory that
Obviates Mathematical Analysis
By Shalosh B. Ekhad (Written April 1, 1998!)
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Constructing Efficient Particle Accelerators is as Easy As 1+1=2
(Thanks to Vladimir Visnjic)
By Doron Zeilberger [ Also in Math. Mag. 72(1999), 151.]
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An Infinite Sequence of Trite but True Sentences
By Doron Zeilberger
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Doron Zeilberger's
Response to the Award of the 1998 AMS Leroy P. Steele award for
Seminal Contributions to Research to Herb Wilf and
Zeilberger
By Doron Zeilberger [Appeared in
Notices of the Amer. Math. Soc. 45(4) (April 1998), 504-508].
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The Integer-Sequence for the Number of Monomer-Dimer Tilings of
an n by n Chessboard Starts With ...
By Shalosh B. Ekhad
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A Very Short Proof of a Short Emperor's Theorem
By Shalosh B. Ekhad
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Test Your C.Q. [Conjecture Quotient]
By Doron Zeilberger
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How Sister Celine Fasenmyer and Dick Duffin Shaped my Mathematical
Personality
By Doron Zeilberger
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The Theory of Self-Avoiding Walks is Only 66.81 Percents Mathematical
(According to the Appel Test).
By Shalosh B. Ekhad
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Research Announcement: The Transcendence of e+Pi and e*Pi
(Written April 1, 1997!)
By Doron Zeilberger
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How Borwein and Bradley's Hypergeometric Ugly Duckling Turned Into
a Beautiful Eulerian Swan, thanks to Almkvist and Granville's Magic
By Doron Zeilberger
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King Solomon and Rabbi ben Ezra's Evaluations of Pi and Patriarch
Abraham's Analysis of an Algorithm
By Doron Zeilberger
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Letter to the Editor of the Monthly About v. 102 isue 10
By Doron Zeilberger
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Yet another proof of Cayley's formula for the number of labelled trees:
By Doron Zeilberger (based on a comment of Herb Wilf)
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The n^(n-2)th proof for the number of labelled trees
By Doron Zeilberger
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A Proof of Morley's Theorem (from the Devil's book)
By Shalosh B. Ekhad
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Proof of the Riemann Hypothesis and other Hitherto Undemonstrated
Propositions (written 4/1/95), by Shalosh B. Ekhad
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A new proof that there 2^n ways to toss a coin n times
By Doron Zeilberger
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A Short proof of Pascal's Hexagon Theorem
By Shalsoh B. Ekhad and Rene Descartes
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The joy of brute force: the covariance of the number of inversions
and the major index By Shalosh B. Ekhad
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A wordy proof of a combinatorial lemma that arose in operator theory
By Doron Zeilberger
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Catalan strikes again (and again)*By Doron Zeilberger
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On a question of Don Knuth
By Doron Zeilberger
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