On linearization coefficients of q-Laguerre polynomials

被引：2

作者：

Hwang, Byung-Hak ^{[1
]}

Kim, Jang Soo ^{[2
]}

Oh, Jaeseong ^{[1
]}

Yu, Sang-Hoon ^{[1
]}

机构：

[1] Seoul Natl Univ, Dept Math, Seoul, South Korea

[2] Sungkyunkwan Univ, Dept Math, Suwon, South Korea

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2020年 / 27卷 / 02期

关键词：

COMBINATORICS; DERANGEMENTS;

D O I：

10.37236/9275

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1 / 21

页数：21

共 15 条

[1] Linearization coefficients for orthogonal polynomials using stochastic processes [J].