Séminaire Lotharingien de Combinatoire, B81e (2020), 20 pp.
Qiongqiong Pan and Jiang Zeng
of (q,y)-Laguerre Polynomials and Their Moments
We consider a (q,y)-analogue of Laguerre polynomials
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
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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