All the papers (and lectures) listed here are exclusively published
in this website
(and many are also in arxiv.org, but not in a "regular" journal), unless
noted otherwise.

Efficient Evaluations of Weighted Sums over the Boolean Lattice inspired by conjectures of Berti, Corsi, Maspero, and Ventura
By Shalosh B. Ekhad and Doron Zeilberger

The JacksonRichmond 4CT Constant is EXACTLY 10/27
By Shalosh B. Ekhad and Doron Zeilberger

Implementing and Experimenting with the CalabiWilf algorithm for random selection of a subspace over a finite field
By Shalosh B. Ekhad and Doron Zeilberger

Explicit Expressions for Moments of the Duration of a 3Player Gambler's Ruin
By Shalosh B. Ekhad and Doron Zeilberger

What is Algebraic Combinatorics and What Should It Be
(talk given to commemorate 30 years of the Journal of Algebraic Combinatorics)
By Doron Zeilberger

Counting Clean Words According to the Number of Their Clean Neighbors
By Shalosh B. Ekhad and Doron Zeilberger

Marko Petkovsek (19552023), My A=B Mate
By Doron Zeilberger

Experimenting with Standard Young Tableaux
By Shalosh B. Ekhad and Doron Zeilberger

Experimenting with the DymLuks Ball and Cell Game (almost) Sixty Years Later
By Shalosh B. Ekhad and Doron Zeilberger

Outline and Links for (an unrecorded Zoom) Talk "Mathematics is an Older Person Game!"
(Purdue History of Mathematics Seminar, Dec. 9, 2022)
By Doron Zeilberger

All the Years when the Z family will have ALL prime Birthdays
By Shalosh B. Ekhad

The Average AMS fellow who died before Aug. 2022 lived 83.36 years, published 98.53 papers, and was cited 2473.23 times
By Livia A. Stone and Doron Zeilberger

A Maple package for Fast Computations of Certain Poincare Series Introduced by Allan Berele in the Theory of Polynomial Identity Rings and Invariant Theory
By Shalosh B. Ekhad and Doron Zeilberger

Computing Determinants Involving Stirling Numbers
By Tewodros Amdeberhan and Shalosh B. Ekhad

Extending the Larcombe Matrix for Cohort Sequences of Solutions of Linear Recurrences with Constant Coefficients to Higher Orders
By Shalosh B. Ekhad

Five More Proofs of the Cosine Addition Formula (Inspired by Mark Levi's Perpetuum Mobile Proof)
By Doron Zeilberger

LinearTime and ConstantSpace Algorithms to compute MultiSequences that arise in Enumerative Combinatorics (and Elsewhere)
By Shalosh B. Ekhad and Doron Zeilberger

A Linear Time, and Constant Space, Algorithm to Compute the Mixed Moments of the Multivariate Normal Distributions
By Shalosh B. Ekhad and Doron Zeilberger

Automated Counting and Statistical Analysis of Labeled Trees with Degree Restrictions
By Shalosh B. Ekhad and Doron Zeilberger

Automating John P. D'Angelo's method to study Complete Polynomial Sequences
By Shalosh B. Ekhad and Doron Zeilberger

An Experimental (yet fully rigorous!) Study of a certain "Measure Of Disarray" that 12year Noga Alon Proved was always Even
By Shalosh B. Ekhad and Doron Zeilberger

Automatic Generation of Convolution Identities for Cfinite sequences
By Shalosh B. Ekhad and Doron Zeilberger

Numeric and Symbolic Programming in Lattice Paths Enumeration
[Videotaped lecture]
By Doron Zeilberger

A OneLine Proof of Leversha's ``Quartet of Isogonal Conjugates" Theorem
By Shalosh B. Ekhad

The Centipede and Braess Paradoxes [Videotaped lecture]
By Doron Zeilberger

Some Deep and Original Questions about the "critical exponents" of Generalized Ballot Sequences
By Shalosh B. Ekhad and Doron Zeilberger

Proof of the Riemann Hypothesis, the NP ≠ P conjecture, the Goldbach Conjecture and the Irrationality of γ
[Videotaped lecture]
By Doron Zeilberger

Automated Generation of Generating Functions Related to Generalized Stern's Diatomic Arrays in the footsteps of Richard Stanley
By Shalosh B. Ekhad and Doron Zeilberger

A Bijective Proof of Richard Stanley's Observation that the sum of the cubes of the nth row of`
Stern's Diatomic array equals 3 times 7^{n1}
By Shalosh B. Ekhad and Doron Zeilberger

How to get the right answer with as few questions as possible? [videotaped lecture]
By Doron Zeilberger

Two Quick Proofs of a Catalan Lemma Needed by Lisa Sauermann and Yuval Wigderson
By Shalosh B. Ekhad and Doron Zeilberger

Automatic Solving of Cubic Diophantine Equations Inspired by Ramanujan
By Shalosh B. Ekhad and Doron Zeilberger

Counting Standard Young Tableaux With Restricted Runs
By Manuel Kauers and Doron Zeilberger

Automatic Counting of Restricted Dyck Paths via (Numeric and Symbolic) Dynamic Programming
By Shalosh B. Ekhad and Doron Zeilberger
A Mathematical Analysis of Mathematical Faculty
By Victoria Chayes, Dodam Ih, Yukun Yao, Doron Zeilberger, and Tianhao Zhang

A new world record for the irrationality measure of Pi (Videotaped lecture) By Doron Zeilberger

The sequence that started it all (Videotaped lecture) By Doron Zeilberger

The AbsentMinded Passengers Problem via Computer Algebra
By Shalosh B. Ekhad and Doron Zeilberger

Algorithmic Proofs of Two Curious Integral Identities of George Gasper and Michael Schlosser
by Shalosh B. Ekhad

Dick Askey: A Special Guru Indeed
by Doron Zeilberger

Using Symbolic Computation to analyze some Children's Board Games
by Shalosh B. Ekhad and Doron Zeilberger

Guessing the Elusive Patterns in the SlaterValez sequence (aka OEIS A081145)
by Shalosh B. Ekhad and Doron Zeilberger

On the Average Maximal Number of Balls in a Bin Resulting from Throwing r Balls into n Bins T times
by Amir BehrouziFar and Doron Zeilberger

A Mathematical Analysis of Mathematical Salaries and More
Victoria Chayes, Tong Cheng, Terence Coelho, Quentin Dubroff, Dodam Ih, Joe Olsen, Jason Saied, Yukun Yao, Doron Zeilberger and Tianhao Zhang

What is Pi and what it is not (a videotaped lecture)
By Doron Zeilberger

Some Remarks on a recent article by J. P. Allouche
By Shalosh B. Ekhad and Doron Zeilberger

A Detailed Analysis of Quicksort Running Time
By Shalosh B. Ekhad and Doron Zeilberger

Answers to Some Questions about Explicit Sinkhorn Limits posed by Mel Nathanson
By Shalosh B. Ekhad and Doron Zeilberger

Explicit Polynomial Expressions for the Enumeration of 3 by 4 and 3 by 5 SemiMagic Rectangles
By Shalosh B. Ekhad and StudentsOfDrZ ExpMathClass

In How many ways can I carry a total of n coins in my two pockets, and have the same amount in both pockets?
By Shalosh B. Ekhad and Doron Zeilberger

The ``Monkey Typing Shakespeare" Problem for Compositions
By Shalosh B. Ekhad and Doron Zeilberger

An UltraFinitistic Foundation of Probability (Videotaped lecture)
By Doron Zeilberger

Proof of a Conjecture of Neil Sloane Concerning Claude Lenormand's
``Raboter" Operation (OEIS sequence A318921)
By Doron Zeilberger
An Experimental Mathematics Approach to Truncated Riemann Zeta Function
Edna L. Jones, Yukun Yao, and Doron Zeilberger
Normalized Iterated Averaging Polygons
By Yonah BiersAriel, Matthew P. Charnley, Brooke Logan, Anthony Zaleski, and Doron Zeilberger

Fractional Counting of Integer Partitions
By Doron Zeilberger and Noam Zeilberger

All the Winning Bites for a by b Chomp for a and b up to 14 and Two Computational Challenges
By Shalosh B. Ekhad and Doron Zeilberger

How Many Exciting Soccer Games are there with score (N+1,N)?
By Doron Zeilberger (Notes of Lecture given at Math Leagues Math Camp, July 23, 2018)

Two Hankel Determinants Dear to Volodia Retakh
By Shalosh B. Ekhad and Doron Zeilberger

A Maple Rendition of George Polya's Elementary Proof of the Modularity of the Theta Function
By Dr. Z.'s Experimental Mathematics Spring 2018 class

On the Intriguing Problem of Counting (n+1,n+2)core partitions into Odd Parts
By Anthony Zaleski and Doron Zeilberger

How Many Rounds Should You Expect in Urn Solitaire?
By Shalosh B. Ekhad and Doron Zeilberger

A Treatise on Sucker's Bets
By Shalosh B. Ekhad and Doron Zeilberger

CNFDNF and all that
(Videotaped Lecture)
By Doron Zeilberger

Automated Generation of Anomalous Cancellations
By Shalosh B. Ekhad

Automated Proofs of Many Conjectured Recurrences in the OEIS made by R.J. Mathar
By Shalosh B. Ekhad, Mingjia Yang and Doron Zeilberger

A 0.2Seconds proof of the Main Result of a 17page Article that Appeared in the May 2017 volume of the journal Advances in Applied Mathematics
By Shalosh B. Ekhad

The Dayenu Boolean Function Is Almost Always True!
By Doron Zeilberger

Counting Permutations that Avoid Many Patterns
By
Yonah BiersAriel, Haripriya Chakraborty, John Chiarelli, Bryan Ek, Andrew Lohr, Jinyoung Park, Justin Semonsen,
Richard Voepel, Mingjia Yang, Anthony Zaleski, and Doron Zeilberger

Automated Derivation of Limiting Distributions Of Combinatorial Random Variables Whose Generating Functions are Rational
By Doron Zeilberger

The Experimental Mathematics of Voting
(Videotaped Lecture)
By Doron Zeilberger

Why the Cautionary Tales Supplied by Richard Guy's Strong Law of Small Numbers Should not be Overstated
By Doron Zeilberger

Automated Proof (or Disproof) of Linear Recurrences Satisfied by Pisot Sequences
By Shalosh B. Ekhad, N. J. A. Sloane and Doron Zeilberger

Jonathan Borwein(19512016) a PiONEER of Experimental Mathematics (Videotaped Lecture)
By Doron Zeilberger

Going Back to Neil Sloane's FIRST LOVE (OEIS Sequence A435): On the Total Heights in Rooted Labeled Trees
By Shalosh B. Ekhad and Doron Zeilberger

A Motivated Rendition of the EllenbergGijswijt Gorgeous proof that the Largest Subset of F_{3}^{n} with No
ThreeTerm Arithmetic Progression is O(c^{n}), with c=2.75510461302363300022127...
By Doron Zeilberger

On the Most CommonlyOccurring Score Vectors of American Tournaments of nplayers, and their Corresponding Records
By Shalosh B. Ekhad

On the number of Singular Vector Tuples of HyperCubical Tensors
By Shalosh B. Ekhad and Doron Zeilberger

Doron Gepner's Statistics on Words in {1,2,3}^{*} is (Most Probably) Asymptotically Logistic
By Doron Zeilberger

Krishna Alladi's Early Love: Irrationality Measures of Famous Constants
[Videotaped lecture]
By Doron Zeilberger

A Diatribe against the "Law" of the Excluded Middle [Videotaped lecture]
By Doron Zeilberger

The Cfinite Ansatz Meets the Holonomic Ansatz
By Shalosh B. Ekhad and Doron Zeilberger

The Babylonian vs. the Greek Approaches to Computer Proofs
[Videotaped Lecture]
By Doron Zeilberger

Computerizing the AndrewsFraenkelSellers Proofs on the Number of mary partitions mod m (and doing MUCH more!)
By Shalosh B. Ekhad and Doron Zeilberger

Searching for Disjoint Covering Systems with Precisely One Repeated Modulus
By Shalosh B. Ekhad, Aviezri S. Fraenkel, and Doron Zeilberger

Doron Zeilberger Interviewed by Ron Aharoni

To Think in a SymbolicComputational Way..
[Videotaped Lecture]
,
By Doron Zeilberger

25 Years of WilfZeilberger Theory in 48 minutes [Videotaped Lecture]
,
By Doron Zeilberger

Explicit Expressions for the Variance and Higher Moments of the Size of a Simultaneous Core Partition and its Limiting Distribution
,
By Shalosh B. Ekhad and Doron Zeilberger

Wilf's "Snake Oil" Method Proves an Identity In The Motzkin Triangle
,
By Tewodros Amdeberhan, Moa Apagodu, and Doron Zeilberger

The BlackScholes Equation WITHOUT Tears (or Probability!)
,
By Doron Zeilberger

Proof of Kyle Petersen's Amazing Conjecture Relating the q and Fibonacci Analogs of n!
,
By Doron Zeilberger

Proofs of the Riemann Hypothesis and of "P is NOT EQUAL to NP" [Videotaped Lecture]
,
By Doron Zeilberger

The number of 1...davoiding permutations of length d+r for SYMBOLIC d but numeric r
,
By Shalosh B. Ekhad, Nathaniel Shar, and Doron Zeilberger

A Very Short (Bijective!) Proof of Touchard's Catalan Identity
,
By Amitai Regev, Nathaniel Shar, and Doron Zeilberger

OddRule Cellular Automata on the Square Grid,
By Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger

A MetaAlgorithm for Creating Fast Algorithms for Counting ON Cells in OddRule Cellular Automata
By Shalosh B. Ekhad, N. J. A. Sloane, and Doron Zeilberger

The Method(!) of "Guess and Check"
By Shalosh B. Ekhad and Doron Zeilberger

Guess and Check(!) [Videotaped Lecture]
By Doron Zeilberger

Generalizing A Putnam 2014 Question
By Tewodros Amdeberhan and Shalosh B. Ekhad

An Empirical Method for Solving (rigorously!) Algebraic Functional Equations Of the Form F(P(x,t), P(x,1),x,t)=0
By Ira M. Gessel and Doron Zeilberger (posted Dec. 28, 2014)

The Generating Functions Enumerating 12..dAvoiding Words with r occurrences of each of 1,2, ..., n are Dfinite for all d and all r
By Shalosh B. Ekhad and Doron Zeilberger (posted Dec. 5, 2014)

A Quick Empirical Reproof of the Asymptotic Normality of the Hirsch Citation Index (First proved by Canfield, Corteel, and Savage)
By Shalosh B. Ekhad and Doron Zeilberger (posted Oct. 31, 2014)

Two Motivated Concrete Proofs (much better than the usual one) that the SquareRoot of 2 is Irrational
By Doron Zeilberger
(posted Oct. 7, 2014)

Some Mathematical Footnotes to Zvi Artstein's Masterpiece ``Mathematics and the Real World"
By Doron Zeilberger
(posted Oct. 7, 2014)

Dominique Foata: A Neoclassical Giant (Videotaped Lecture)
By Doron Zeilberger
(posted Oct. 2, 2014)

Sketch of a Proof of an Intriguing Conjecture of Karola Mészáros and Alejandro Morales
Regarding the Volume of the D_{n} Analog of the ChanRobbinsYuen Polytope
By Doron Zeilberger
(posted July 10, 2014)

There are
(r+1)(r+2)(2r+3)(r^{2}+3r+5) Ways For the Four Teams
of a World Cup Group
to Each Have r Goals For
and r Goals Against
[Thanks to the Soccer Analog of Prop. 4.6.19 of Richard Stanley's (Classic!) EC1]
By Shalosh B. Ekhad and Doron Zeilberger
(posted July 7, 2014)

Enumerative Geometrical Genealogy (Or: The Sex Life of Points and Lines)
By Shalosh B. Ekhad and Doron Zeilberger
(posted June 19, 2014)

Statistical Analysis of the Ages of Noah's MALE Ancestors and a Probabilistic
Proof That Enoch's Premature Death was Indeed an Act of God
By Shalosh B. Ekhad
(posted June 4, 2014)

Searching for ApéryStyle Miracles [Using, InterAlia, the Amazing AlmkvistZeilberger Algorithm]
By Shalosh B. Ekhad and Doron Zeilberger
(posted May 17, 2014)

The Past and Future of Enumerative Combinatorics
[Videotaped Lecture]
By Doron Zeilberger (posted April 7, 2014)

Automatic Proofs of Asymptotic ABNORMALITY (and much more!) of Natural Statistics Defined on CatalanCounted Combinatorial Families
By Shalosh B. Ekhad and Doron Zeilberger
(posted March 21, 2014)

How to get Better and Better Rational Approximations to Pi Without Cheating By Shalosh B. Ekhad (posted March 14, 2014)

Proofs are dead, long live algorithms
[Videotaped Lecture]
By Doron Zeilberger (posted Feb. 18, 2014)

Two OneLine Proofs of Heron's Formula that Says that the AreaSquared of a Triangle is
(a+b+c)(a+bc)(a+cb)(b+ca)/16 By Shalosh B. Ekhad and Doron Zeilberger (posted Jan. 20, 2014) .

A Conjectured Explicit Determinant Evaluation Whose Proof Would Make Us Happy (and the OEIS richer)
By Douglas Hofstadter and Doron Zeilberger (posted Jan. 7, 2014, revised April 17, 2014)

George Eyre Andrews (b. Dec. 4, 1938): A Reluctant REVOLUTIONARY
[Videotaped Lecture]
By Doron Zeilberger (posted Dec. 10, 2013)

How to Extend Károlyi and Nagy's BRILLIANT Proof of the
ZeilbergerBressoud qDyson Theorem in order to Evaluate ANY Coefficient of the qDyson Product
By Shalosh B. Ekhad and Doron Zeilberger (posted Aug. 15, 2013)

Generalizing and Implementing Michael Hirschhorn's AMAZING Algorithm for Proving RamanujanType Congruences
By Edinah K. Gnang and Doron Zeilberger (posted June 27, 2013)

On a Conjecture of Melkamu Zeleke
By Shalosh B. Ekhad (posted April 19, 2013)

A Short Proof of a PtolemyLike Relation for an Even number of Points
on a Circle Discovered by Jane McDougall
By Marc Chamberland and Doron Zeilberger (posted April 16, 2013)
[Also appeared (with a shorter title) in Amer. Mathematical Monthly v. 121(2014), 263265]

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 SomosLike Miracles as You Wish
By Shalosh B. Ekhad and Doron Zeilberger (posted March 21, 2013)
[Also appeared in J. Difference Equations and Applications 20 (2014), 852858 (in a special issue in honor of Gerry Ladas)]

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 TwoCircle 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 FlajoletSedgewick Chefd'œuvre]
By Shalosh B. Ekhad and Doron Zeilberger(posted Dec. 17, 2012)

Pick Up Sticks
By Larry Shepp, Doron Zeilberger, and CunHui Zhang (posted Oct. 16, 2012)

The Amazing 3^{n} 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 socalled 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 mDimensional Partitions of Eleven and Twelve
By Shalosh B. Ekhad (Written Feb. 15, 2012)

A Maple OneLine Proof of George Andrews's Formula that Says that the Number
of Triangles with Integer Sides Whose Perimeter is
n Equals {n^{2}/12} [n/4][(n+2)/4]
By Shalosh B. Ekhad (Written Feb. 6, 2012)

Using GENERATINGFUNCTIONOLOGY to Enumerate DistinctMultiplicity Partitions
By Doron Zeilberger (Written Jan. 18, 2012)

Another Hanukkah Miracle: The Gaps Between Consecutive ChristmasinHanukkah Years is ALWAYS a Fibonacci Number! (2nd ed.)
By Lisa Budd and Shalosh B. Ekhad
First edition (only be SBE) : Jan. 2, 2012. This second edition: Nov. 15, 2019.

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 OneLiner 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 npermutations that contain the Pattern 321 Exactly Once
Equals (3/n)(2n)!/((n3)!(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 ExperimentalMathematical Proof)
By Shalosh B. Ekhad (Written June 28, 2011).

Two Proofs that Σ_{k} (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 SameSex 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 SaganSavage LucasCatalan 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 (19302010) 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 SymbolCrunching 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 RUMath640(Sp2010)
(published April 10, 2010).

The Number of Inversions and the Major Index of Permutations are Asymptotically JointIndependently 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 MultiSet 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 ComputerGenerated 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' qTSPP 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 RazumovStroganov 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 dDimensional Manhattan)
by Doron Zeilberger (Written: Dec. 18, 2007).

The Number of Ways of Walking in
x_{1} ≥ ... ≥ x_{k} ≥ 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
nCell 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 ZinnJustin
related to the qKZ equations and to
Dave Robbins' Two Favorite Combinatorial Objects
by Doron Zeilberger (Written: March 20, 2007).

Martin KRUSKAL(Sept. 28, 1925Dec.26, 2006) and
Peter HAMMER(Dec. 23, 1936Dec. 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 ThreeRowed 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 LoehrWarrington Amazing TEN to the Power n Conjecture
by Shalosh B. Ekhad, Vince Vatter and Doron Zeilberger .
[ copublished 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 NoLongerSoAmazing LoehrWarrington
Lattice Paths Conjecture
by Doron Zeilberger
(Written: Oct. 23, 2005).

A Snappy Proof That 123Avoiding Words are Equinumerous With 132Avoiding
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, MarchApril 2005 issue].

How Adam Marcus and Gabor Tardos Divided and Conquered the StanleyWilf
Conjecture (An Étude in Paramathematics)
by
Doron Zeilberger (Written: Oct. 20, 2004).

A 360Character Maple Code that Proves (in 0.05 Seconds!) Sergey Sadov's
Ptolemytype 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" ComputerDiscovered [and ComputerProved!] Hypergeometric
Series Evaluations.
by
Shalosh B. Ekhad (Written: Oct. 12, 2004).

A FibonacciCounting Proof Begged by Benjamin and Quinn
by
Doron Zeilberger (Written: May 24, 2004).

A Loving Rendition of the MarcusTardos Amazing Proof of the
FürediHajnal 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 AgmonKannai 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 (19552000): 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 OneLine Proof of a Partition Theorem
Generated by AndrewsPauleRiese's Computer
Reported by Doron Zeilberger.

A 2Minute Proof of the 2ndMost Important Theorem of the
2nd Millenium
By Doron Zeilberger.

The Generalized U2Flashlight Microsoft 5Minute 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, SepDec. (1998) 382385)

``A Heterosexual Mehler Formula for the Straight Hermite Polynomials
(A La Foata)''
By
Doron Zeilberger.

Aufgabe VII.47 of PolyaSzego Immediately Implies Dave Robbins's
MultiIntegral 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), 504508].

The IntegerSequence for the Number of MonomerDimer 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 SelfAvoiding 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)

Lagrange Inversion Without Tears (Analysis) (based on Henrici)
By Doron Zeilberger

The n^(n2)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.)