On linearization coefficients of q-Laguerre polynomials
Abstract
The linearization coefficient L(Ln1(x)… Lnk(x)) of classical Laguerre polynomials Ln(x) is known to be equal to the number of (n1,…,nk)-derangements, which are permutations with a certain condition. Kasraoui, Stanton and Zeng found a q-analog of this result using q-Laguerre polynomials with two parameters q and y. Their formula expresses the linearization coefficient of q-Laguerre polynomials as the generating function for (n1,…,nk)-derangements with two statistics counting weak excedances and crossings. In this paper their result is proved by constructing a sign-reversing involution on marked perfect matchings.
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