91 citations · 520 across the 230 of their papers we have counts for
12 papers · 1 filter
An Empirical Method for Solving (rigorously!) Algebraic Functional Equations Of the Form F(P(x,t), P(x,1),x,t)=0
Ira M. Gessel, Doron Zeilberger
We present an empirical-yet-rigorous approach for solving a wide class of functional equations, thereby automating many results that previously required considerable human ingenuit…
The Generating Functions Enumerating 12..d-Avoiding Words with r occurrences of each of 1,2, ... , n are D-finite for all d and all r
Shalosh B. Ekhad, Doron Zeilberger
In this article, dedicated with admiration and gratitude to guru Neil Sloane on his 75-th birthday, we observe that the generating functions for multi-set permutations that do not…
The (Ordinary) Generating Functions Enumerating 123-Avoiding Words with r occurrences of each of 1,2, ..., n are Always Algebraic
Nathaniel Shar, Doron Zeilberger
Recently, Bill Chen, together with his disciples Alvin Dai and Robin Zhou, discovered, and very elegantly proved, an algebraic equation satisfied by the generating function enumera…
A Quick Empirical Reproof of the Asymptotic Normality of the Hirsch Citation Index (First proved by Canfield, Corteel, and Savage)
Shalosh B. Ekhad, Doron Zeilberger
Once upon a time there was an esoteric and specialized notion, called "size of the Durfee square", of interest to at most 100 specialists in the whole world. Then it was kissed by…
Two Motivated Concrete Proofs (much better than the usual one) that the Square-Root of 2 is Irrational
Doron Zeilberger
This short "education note" was inspired by Zvi Artstein's masterpiece Mathematics and the Real World, the Remarkable Role of Evolution in the Making of Mathematics (p. 53, and p.…
Sketch of a Proof of an Intriguing Conjecture of Karola Meszaros and Alejandro Morales Regarding the Volume of the Analog of the Chan-Robbins-Yuen Polytope (Or: The Morris-Selberg Constant Term Identity Strikes Again!)
Doron Zeilberger
Using the Morris-Selberg Constant Term Identity, I sketch a proof of a recent conjecture by Karola Meszaros and Alejandro Morales, that I believe could be easily made fully rigorou…