Some Deep and Original Questions about the "critical exponents" of Generalized Ballot Sequences

By Shalosh B. Ekhad and Doron Zeilberger

.pdf   .tex  

(Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger and

Written: April 4, 2021.

We numerically estimate the critical exponents of certain enumeration sequences that naturally generalize the famous Catalan and super-Catalan sequences, and raise deep and original questions about their exact values, and whether they are rational numbers.

Added April 7, 2021: Michael Wallner proved that indeed none of these sequences are P-recursive (in the 3D case) and none of the critical exponents are rational numbers, completely answering (in the 3D case) the deep and original questions raised in the article.

read his insightful Email message

Michael Wallner plans to write it up as a short note for the arxiv. As soon as it is there, I will make the promised donation to the OEIS in his honor.

Added May 27, 2021: Michael Wallner just posted his beautiful artice. A donation to the OEIS, in his honor, has been made.

Maple package

Sample Input and Output files for Capone.txt

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

Doron Zeilberger's Home Page