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arXiv · 1901.00907

Combinatorics of $(q,y)$-Laguerre polynomials and their moments

Qiongqiong Pan·Jiang Zeng
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Abstract

We consider a $(q,y)$-analogue of Laguerre polynomials $L^{(\alpha)}_n(x;y;q)$ for integral $\alpha\geq -1$, which turns out to be a rescaled version of Al-Salam--Chihara polynomials. A combinatorial interpretation for the $(q,y)$-Laguerre polynomials is given using a colored version of Foata-Strehl's Laguerre configurations with suitable statistics. When $\alpha\geq 0$, the corresponding moments are described using certain classical statistics on permutations, and the linearization coefficients are proved to be a polynomial in $y$ and $q$ with nonnegative integral coefficients.

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Qiongqiong Pan, Jiang Zeng. 2019-01-03. Combinatorics of $(q,y)$-Laguerre polynomials and their moments. https://arxiv.org/abs/1901.00907

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