Séminaire Lotharingien de Combinatoire, B81e (2020), 20 pp.

Qiongqiong Pan and Jiang Zeng

Combinatorics of (q,y)-Laguerre Polynomials and Their Moments

Abstract. We consider a (q,y)-analogue of Laguerre polynomials L(α)n(x;y|q) for integral α >= -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 and Strehl's Laguerre configurations with suitable statistics. When α >= 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.

Received: April 7, 2019. Accepted: January 23, 2020.

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