All the papers (and lectures) listed here are exclusively published
in this website
(and some also in arxiv.org, but not in a "regular" journal), unless
noted otherwise.
-
On a Conjecture of Melkamu Zeleke
By Shalosh B. Ekhad (posted April 19, 2013)
-
A Short Proof of a Ptolemy-Like Relation for an Even number of Points
on a Circle Discovered by Jane McDougall
By Marc Chamberland and Doron Zeilberger (posted April 16, 2013)
-
On Euler's "Misleading Induction", Andrews' "Fix", and How to Fully Automate them
By Shalosh B. Ekhad and Doron Zeilberger (posted April 3, 2013)
-
How To Generate As Many Somos-Like Miracles as You Wish
By Shalosh B. Ekhad and Doron Zeilberger (posted March 21, 2013)
-
How I Need a Drink, Alcoholic Of Course, After the Heavy Lectures Involving ... (Videotaped lecture)
By Doron Zeilberger (posted March 20, 2013)
-
A Quick (.1 seconds!) Proof of Gigoujeu's Two-Circle Theorem
By Shalosh B. Ekhad (posted March 17, 2013)
-
A (Human!) Proof of A Conjectured Triple Sum Identity Made By Juan Sebastian Pereyra
By Doron Zeilberger (posted March 5, 2013)
-
A Proof in the Style of George Andrews
(and G. H. Hardy, and Unfortunately MANY other, otherwise very smart, people) that
1+1+...+1 (n+1 times)= n+1
By Doron Zeilberger(posted Jan. 3, 2013)
-
Automated Counting of Towers (À La Bordelaise)
[Or: Footnote to p. 81 of the Flajolet-Sedgewick Chef-d'œuvre]
By Shalosh B. Ekhad and Doron Zeilberger(posted Dec. 17, 2012)
-
Pick Up Sticks
By Larry Shepp, Doron Zeilberger, and Cun-Hui Zhang (posted Oct. 16, 2012)
-
The Amazing 3n Theorem
and its even more Amazing Proof [Discovered by Xavier G. Viennot and his École Bordelaise gang]
By Doron Zeilberger (posted Aug. 10, 2012)
-
Joyal's Proof of Cayley's Formula
By Gyu Eun Lee and Doron Zeilberger (posted July 18, 2012)
-
The Rise and Fall of Astrology and the Future Fall of the so-called Infinity(Videotaped lecture)
By Doron Zeilberger (posted March 29, 2012)
-
The Joy of Dreaming to be Famous (Videotaped lecture)
By Doron Zeilberger (posted March 1, 2012)
-
The Composition Enumeration Reciprocity Theorem
By Doron Zeilberger (Written Feb. 28, 2012)
-
Computational and Theoretical Challenges on
Counting Solid Standard Young Tableaux
By Shalosh B. Ekhad and Doron Zeilberger (Written Feb. 20, 2012)
-
The number of m-Dimensional Partitions of Eleven and Twelve
By Shalosh B. Ekhad (Written Feb. 15, 2012)
-
A Maple One-Line Proof of George Andrews's Formula that Says that the Number
of Triangles with Integer Sides Whose Perimeter is
n Equals {n2/12} -[n/4][(n+2)/4]
By Shalosh B. Ekhad (Written Feb. 6, 2012)
-
Using GENERATINGFUNCTIONOLOGY to Enumerate Distinct-Multiplicity Partitions
By Doron Zeilberger (Written Jan. 18, 2012)
-
Another Hanukkah Miracle: The Gaps Between Consecutive Christmas-in-Hanukkah Years is ALWAYS a Fibonacci Number!
By Shalosh B. Ekhad (Written Jan. 2, 2012)
-
Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610
and ANY Problem of That Type
By Shalosh B. Ekhad and Doron Zeilberger (Written Dec. 28, 2011)
-
The [NameRemoved] Determinant Identity is Purely Routine
By Doron Zeilberger (Written Dec. 23, 2011)
-
The Binomial Theorem for (N+n)r (where Nf(n)=f(n+1))
By Moa Apagodu, Shalosh B. Ekhad, and Patrick Gaskill
[Added Dec. 13, 2011: scooped by Koutschan et. al.'s paper]
-
A Tribute to Herb Wilf
By Doron Zeilberger(Written Dec. 7, 2011, to be copublished in the W80 proceedings volume)
-
The Simplest Proof That Phi Is Irrational
By Zehava Yachas (Written Nov. 21, 2011)
-
Amanda Folsom and Ken Ono's Error Could Have (and Should Have!)
been Discovered by Their Computers (in Less than Three Seconds!)
By Shalosh B. Ekhad (Posted Nov. 18, 2011).
-
A Maple One-Liner that is a MUCH Better ANSWER than
George Andrews' ``Explicit'' Formula for the Rademacher Coefficients
By Shalosh B. Ekhad (Written Oct. 23, 2011).
-
Alexander Burstein's Lovely Combinatorial Proof of John Noonan's Beautiful Formula
that the number of n-permutations that contain the Pattern 321 Exactly Once
Equals (3/n)(2n)!/((n-3)!(n+3)!)
By Doron Zeilberger (Written Oct. 18, 2011).
Table of Natural Logarithms of All Integers from 1 to 50000
By Shalosh B. Ekhad (Generated Sept. 14, 2011).
-
The Expected Number of Blocks in an Ordered Set Partition of n objects is n/log(4)+O(1),
its Variance is (n/log(4))(1/log(4)-1/2)+O(1),
and It is Asymptotically Normal! (An Experimental-Mathematical Proof)
By Shalosh B. Ekhad (Written June 28, 2011).
-
Two Proofs that Σk (-1)k k!S(n,k)=(-1)n
By Doron Zeilberger (Written June 26, 2011).
-
In How Many Ways Can the Chess Pieces Walk n Steps, Staying on the Board? By Shalosh B. Ekhad
(Generated May 19, 2011)
-
Automatic Generation of Generating Functions for Enumerating Matchings
By Shalosh B. Ekhad and Doron Zeilberger
(Written April 29, 2011)
-
The Number of Same-Sex Marriages in a Perfectly Bisexual Population is
Asymptotically Normal
By Shalosh B. Ekhad
(Written April 28, 2011)
-
In How Many Ways Can a King Return Home After Walking n Steps?
By Shalosh B. Ekhad
(Written April 13, 2011)
-
The Sum of Two and Seven and The Product of Three by Three
By Semaj Srelles
(Written April 12, 2011)
-
Automatic Generation of Generating Functions for Counting
the Number of Spanning Trees for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
By Shalosh B. Ekhad and Doron Zeilberger
(Written April 2, 2011)
-
Automatic Generation of Generating Functions for Chromatic Polynomials
for Grid Graphs (and more general creatures) of Fixed (but arbitrary!) Width
By Shalosh B. Ekhad, Jocelyn Quaintance, and Doron Zeilberger
(Written March 30, 2011)
-
A Note on an American Mathematical Monthly Note
By Doron Zeilberger
(Written Feb. 11, 2011)
-
The Sagan-Savage Lucas-Catalan Polynomials Have Positive Coefficients
By Shalosh B. Ekhad
(Written Jan. 17, 2011)
-
The Maximal number of floors a Building can have ...
By Shalosh B. Ekhad
(Written Nov. 7, 2010)
-
A Case Study in Experimental (Yet Fully Rigorous!) Mathematics (Videotaped Lecture)
By Doron Zeilberger
(delivered Nov. 4, 2010, posted Nov. 6, 2010).
-
Play Time With Determinants
By Tewodros Amdeberhan and Shalosh B. Ekhad (with an appendix by Christoph Koutschan and his computer)
(Written Oct. 31, 2010)
-
Leon Ehrenpreis (1930-2010) A truly FUNDAMENTAL
Mathematician (a Videotaped lecture)
By Doron Zeilberger (posted Sept. 22, 2010, delivered Sept. 16, 2010).
-
Why Is it So Hard to Count? (Videotaped Lecture)
By Doron Zeilberger (posted Sept. 2, 2010, delivered Aug. 14, 2010).
-
HISTABRUT: A Maple Package for Symbol-Crunching in Probability theory
By Doron Zeilberger (Published: Aug. 25, 2010).
-
Refined Asymptotics and Explicit Recurrences for the numbers of Young tableaux in the (k,l) hook for k+l ≤ 5
By Shalosh B. Ekhad and Amitai Regev (Published: July 28, 2010).
-
3x+1 (Videtape of the 2010 Erdos Memorial Lecture)
By Doron Zeilberger (posted May 21, 2010, produced by Mike McKenna and Marc Heft).
(
reanactment (producted by Edinah Gnang))
-
Bijections for an identity of Young Tableaux
By Amitai Regev and Doron Zeilberger .
(Written: Feb. 22, 2010. Published: May 2, 2010).
-
Statistical Analysis of the Erdos, Zeilberger, and Shelah Numbers
in the Audience in Doron Zeilberger's Erdos Memorial Lecture
By Shalosh B. Ekhad and the students of RU-Math640(Sp2010)
(published April 10, 2010).
-
The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal
(Second Edition!) By Andrew Baxter and Doron Zeilberger
(First edition written April 7, 2010. Second (fully refereed!) edition published Feb. 4, 2011).
-
Experimental Mathematics: Alias, the Future of Mathematics (Videotaped Lecture)
By Doron Zeilberger (posted March 23, 2010, produced by Edinah Gnang).
-
binomial(5,2) Proofs that binomial(n,k) ≤ binomial(n,k+1) if k < n/2
By Doron Zeilberger
(published March 4, 2010).
-
A Note on the Stanley Distribution
By Shalosh B. Ekhad
(published Jan. 20, 2010).
-
A Eulogy for Jack Good
By Doron Zeilberger
(published Dec. 2, 2009).
-
You Don't Have To Be an Einstein to Figure Out that Sara Should (Asymptotically) Eat
n/3+4/27+O(1/n) Dove Bars ...
By Shalosh B. Ekhad
(published Nov. 11, 2009).
-
A Multi-Set Identity for Partitions
By Amitai Regev and Doron Zeilberger
(posted here Sept. 22, 2009).
In How Many Ways Can You Reassemble Several Russian Dolls?
By Doron Zeilberger (published Sept. 16, 2009).
A Computer-Generated Proof that P=NP
By Doron Zeilberger (published April 1(!), 2009).
An Inelegant (but Short(!)) Proof of a Major Index Theorem of Garsia and Gessel
By Doron Zeilberger (published March 29, 2009).
The Number of Walks on a Regular Cayley Tree
By Eric Rowland and Doron Zeilberger (published March 12, 2009).
A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture
(modulo a finite amount of routine calculations)
By Manuel Kauers, Christoph Koutschan, and Doron Zeilberger
(Written Aug. 2, 2008; Published: Jan. 25, 2009)
-
A Bijectional Attack on the Razumov-Stroganov Conjecture
By Arvind Ayyer and Doron Zeilberger (Written: Dec. 2, 2008)
-
AsyRec: A Maple package for Computing the
Asymptotics of Solutions of Linear Recurrence Equations
with Polynomial Coefficients
by Doron Zeilberger (Written: April 6, 2008).
-
Four Solutions to David Beckwith's
American Mathematical Monthly Problem 11343 (Feb. 2008)
Compiled by Doron Zeilberger (Written: Feb. 8, 2008).
-
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).
-
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).
-
by Doron Zeilberger (Written: June 15, 2007).
-
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).
-
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).
-
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).
-
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).
-
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).
-
Fully AUTOMATED Computerized Redux of Feller's (v.1) Ch. III (and Much More!)
by Doron Zeilberger (Written: Nov. 14, 2006).
-
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.]
-
What Is Experimental Mathematics?
by Doron Zeilberger
(Written: April 4, 2006).
-
Proof of the Celebrated Goldbach's Theorem
by Doron Zeilberger
(Written: April 1, 2006).
-
Automatic CounTilings
by Doron Zeilberger
(Written: Jan. 20, 2006)
-
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).
-
An Umbral Approach to the Hankel Trasform for Sequences
by Doron Zeilberger
(Written: Nov. 7, 2005).
-
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).
-
A Snappy Proof That 123-Avoiding Words are Equinumerous With 132-Avoiding
Words
by
Doron Zeilberger
(Written: April 11, 2005).
-
A Perfect Rhythmic Tilings of QUADRUPLETS
by
Shalosh B. Ekhad and Lara Pudwell
(Written: Nov. 30, 2004).
-
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].
-
How Adam Marcus and Gabor Tardos Divided and Conquered the Stanley-Wilf
Conjecture (An Étude in Paramathematics)
by
Doron Zeilberger (Written: Oct. 20, 2004).
-
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).
-
Forty "Strange" Computer-Discovered [and Computer-Proved!] Hypergeometric
Series Evaluations.
by
Shalosh B. Ekhad (Written: Oct. 12, 2004).
-
A Fibonacci-Counting Proof Begged by Benjamin and Quinn
by
Doron Zeilberger (Written: May 24, 2004).
-
A Loving Rendition of the Marcus-Tardos Amazing Proof of the
Füredi-Hajnal Conjecture
by
Doron Zeilberger (Written: Nov. 30, 2003).
-
All the Moments of the Vertex Degrees of Randomly Generated Graphs
by
Doron Zeilberger (Written: Nov. 30, 2003).
-
Review of George Szpiro's `Kepler's Conjecture'
by
Doron Zeilberger (published in Science, Aug. 29, 2003).
-
Towards a SymbolicComputational Philosophy (and Methodology!) for
Mathematics
by Doron Zeilberger. (Written: Dec. 12, 2002).
-
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).
-
How Many Singles, Doubles, Triples, Etc. Should The Coupon
Collector Expect
by
Doron Zeilberger (Written: July 5, 2001).
-
R(n,n) IS LESS THAN A CONSTANT TIMES (3.9999999999999997)**n
by Shalosh B. Ekhad and
Doron Zeilberger (Written: April 1, 2001!).
-
The Umbral Transfer Matrix Method: II. Counting Plane Partitions
by Doron Zeilberger (Written: Oct. 26, 2000) .
-
Remarks On The PARRONDO PARADOX
by Shalosh B. Ekhad and Doron Zeilberger (Written: Oct. 13, 2000) .
-
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) .
-
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)
-
RODICA SIMION (1955-2000): An (almost) Perfect Enumerator
and Huamn Being
by Doron Zeilberger (Written: Jan. 12, 2000) .
-
Does Dreidel Last O(NUTS**2) Spins?
by Doron Zeilberger (Written: Kislev 30, 5760) .
-
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.) .
-
The Mathematics Behind the Proposed Reform of the Hebrew Calendar
by Doron Zeilberger ( released April 1, 1999!).
-
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 .)
-
A User's Manual for RORTY: A Maple Package for Finding the Final
Vocabularies of Texts.
by Shalosh B. Ekhad and Doron Zeilberger.
-
Some Stretching, Squeezing and Folding Caused By John Allen Paulos's
Masterpiece `Once Upon a Number'.
by Doron Zeilberger.
-
WZ Theory, Chapter II
by Doron Zeilberger.
-
Sylvie Corteel's One-Line Proof of a Partition Theorem
Generated by Andrews-Paule-Riese's Computer
Reported by Doron Zeilberger.
-
A 2-Minute Proof of the 2nd-Most Important Theorem of the
2nd Millenium
By Doron Zeilberger.
-
The Generalized U2-Flashlight Microsoft 5-Minute Puzzle
By Shalosh B. Ekhad and Doron Zeilberger.
-
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)
-
``A Heterosexual Mehler Formula for the Straight Hermite Polynomials
(A La Foata)''
By
Doron Zeilberger.
-
Aufgabe VII.47 of Polya-Szego Immediately Implies Dave Robbins's
Multi-Integral Evaluation
By Doron Zeilberger
-
Mathematical Genitalysis: A Powerful New Combinatorial Theory that
Obviates Mathematical Analysis
By Shalosh B. Ekhad (Written April 1, 1998!)
-
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.]
-
An Infinite Sequence of Trite but True Sentences
By Doron Zeilberger
-
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].
-
The Integer-Sequence for the Number of Monomer-Dimer Tilings of
an n by n Chessboard Starts With ...
By Shalosh B. Ekhad
-
A Very Short Proof of a Short Emperor's Theorem
By Shalosh B. Ekhad
-
Test Your C.Q. [Conjecture Quotient]
By Doron Zeilberger
-
How Sister Celine Fasenmyer and Dick Duffin Shaped my Mathematical
Personality
By Doron Zeilberger
-
The Theory of Self-Avoiding Walks is Only 66.81 Percents Mathematical
(According to the Appel Test).
By Shalosh B. Ekhad
-
Research Announcement: The Transcendence of e+Pi and e*Pi
(Written April 1, 1997!)
By Doron Zeilberger
-
How Borwein and Bradley's Hypergeometric Ugly Duckling Turned Into
a Beautiful Eulerian Swan, thanks to Almkvist and Granville's Magic
By Doron Zeilberger
-
King Solomon and Rabbi ben Ezra's Evaluations of Pi and Patriarch
Abraham's Analysis of an Algorithm
By Doron Zeilberger
-
Letter to the Editor of the Monthly About v. 102 issue 10
By Doron Zeilberger
-
Yet another proof of Cayley's formula for the number of labelled trees:
By Doron Zeilberger (based on a comment of Herb Wilf)
-
The n^(n-2)th proof for the number of labelled trees
By Doron Zeilberger
-
A Proof of Morley's Theorem (from the Devil's book)
By Shalosh B. Ekhad
-
Proof of the Riemann Hypothesis and other Hitherto Undemonstrated
Propositions (written 4/1/95), by Shalosh B. Ekhad
-
A new proof that there are 2^n ways to toss a coin n times
By Doron Zeilberger
-
A Short proof of Pascal's Hexagon Theorem
By Shalsoh B. Ekhad and Rene Descartes
-
The joy of brute force: the covariance of the number of inversions
and the major index By Shalosh B. Ekhad
-
A wordy proof of a combinatorial lemma that arose in operator theory
By Doron Zeilberger
-
Catalan strikes again (and again)*By Doron Zeilberger
-
On a question of Don Knuth
By Doron Zeilberger
-
A Recursive Formulation of Sylvester's Bijection Between
Odd and Distinct Partitions
By Doron Zeilberger (originally written: ca. 1984, posted in this
Personal Journal: Jan. 3, 2011.)