English

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

Combinatorics 2021-05-31 v2 Mathematical Physics math.MP

Abstract

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. In this version we announce that our questions were brilliantly answered by Michael Wallner, and that the pledged donation to the OEIS, in his honor, was made.

Keywords

Cite

@article{arxiv.2104.01731,
  title  = {Some Deep and Original Questions about the "critical exponents" of Generalized Ballot Sequences},
  author = {Shalosh B. Ekhad and Doron Zeilberger},
  journal= {arXiv preprint arXiv:2104.01731},
  year   = {2021}
}

Comments

9 pages; Accompanied by a Maple package and output files available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/capone.html