On linearization coefficients of q-Laguerre polynomials

The linearization coefficient G(L-n1 (x) . . . L-nk (x)) of classical Laguerre polynomials L-n(x) is known to be equal to the number of (n(1), ..., n(k))-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 (n(1), ..., n(k) )-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.