On linearization coefficients of q-Laguerre polynomials

Byung Hak Hwang; Jang Soo Kim; Jaeseong Oh; Sang Hoon Yu

On linearization coefficients of q-Laguerre polynomials

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

Department of Mathematics

Seoul National University

Research output: Contribution to journal › Article › peer-review

Abstract

The linearization coefficient L(L_n₁(x)… L_{n_k} (x)) of classical Laguerre polynomials L_n(x) is well known to be equal to the number of (n₁,…, n_k)-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,…, 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.

Original language	English
Article number	55
Journal	Seminaire Lotharingien de Combinatoire
Issue number	84
State	Published - 2020

Keywords

Laguerre polynomials
linearization coefficient
orthogonal polynomials
sign-reversing involution

Cite this

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title = "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.",

keywords = "Laguerre polynomials, linearization coefficient, orthogonal polynomials, sign-reversing involution",

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year = "2020",

language = "English",

journal = "Seminaire Lotharingien de Combinatoire",

issn = "1286-4889",

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T1 - On linearization coefficients of q-Laguerre polynomials

AU - Hwang, Byung Hak

AU - Kim, Jang Soo

AU - Oh, Jaeseong

AU - Yu, Sang Hoon

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Laguerre polynomials

KW - linearization coefficient

KW - orthogonal polynomials

KW - sign-reversing involution

UR - https://www.scopus.com/pages/publications/85169506781

M3 - Article

AN - SCOPUS:85169506781

SN - 1286-4889

JO - Seminaire Lotharingien de Combinatoire

JF - Seminaire Lotharingien de Combinatoire

IS - 84

M1 - 55

ER -

On linearization coefficients of q-Laguerre polynomials

Abstract

Keywords

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