The MacMahon $q$-Catalan is convex

Tewodros Amdeberhan

The MacMahon $q$-Catalan is convex

Combinatorics 2023-09-06 v2 Number Theory

Authors: Tewodros Amdeberhan

Abstract

Let $n\geq2$ be an integer. In this paper, we study the convexity of the so-called MacMahon's $q$ -Catalan polynomials $C_n(q)=\frac1{[n+1]_q}\left[ 2n \atop n \right]_q$ as functions of $q$ . Along the way, several intermediate results on inequalities are presented including a commentary on the convexity of the generation function for the integer partitions.

Keywords

q-series and q-analogues convex analysis

Cite

@article{arxiv.1608.06032,
  title  = {The MacMahon $q$-Catalan is convex},
  author = {Tewodros Amdeberhan},
  journal= {arXiv preprint arXiv:1608.06032},
  year   = {2023}
}

Comments

New co-authors added, text changed substantially

Related papers

View all related →