Séminaire Lotharingien de Combinatoire, 84B.55 (2020), 12 pp.

Byung-Hak Hwang, Jang Soo Kim, Jaeseong Oh and Sang-Hoon Yu

On Linearization Coefficients of q-Laguerre Polynomials

Abstract. The linearization coefficient L(Ln1(x) ... Lnk(x)) of classical Laguerre polynomials Ln(x) is well known to be equal to the number of (n1,...,nk)-derangements, which are permutations with a certain condition. Kasraoui, Zeng and Stanton 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.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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