A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers

Frédéric Chapoton; Jiang Zeng

A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers

Combinatorics 2013-12-17 v2

Authors: Frédéric Chapoton , Jiang Zeng

Abstract

We study a polynomial sequence $C_n(x|q)$ defined as a solution of a $q$ -difference equation. This sequence, evaluated at $q$ -integers, interpolates Carlitz-Riordan's $q$ -ballot numbers. In the basis given by some kind of $q$ -binomial coefficients, the coefficients are again some $q$ -ballot numbers. We obtain in a combinatorial way another curious recurrence relation for these polynomials.

Keywords

polynomial interpolation Carlitz-Riordan q-ballot numbers q-difference equation q-binomial coefficients combinatorial recurrence q-integers

Cite

@article{arxiv.1311.7228,
  title  = {A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers},
  author = {Frédéric Chapoton and Jiang Zeng},
  journal= {arXiv preprint arXiv:1311.7228},
  year   = {2013}
}

Comments

15 pages, some connections with J. Cigler's earlier work is mentioned

A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers

Abstract

Keywords

Cite

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