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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