Geodesic
On linearization coefficients of \(q\)-Laguerre polynomials
Byung-Hak Hwang ; Jang Soo Kim ; Jaeseong Oh1 ; Sang-Hoon Yu
1Seoul National University
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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The linearization coefficient $\mathcal{L}(L_{n_1}(x)\dots L_{n_k}(x))$ of classical Laguerre polynomials $L_n(x)$ is known to be equal to the number of $(n_1,\dots,n_k)$-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 $(n_1,\dots,n_k)$-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.
DOI : 10.37236/9275
Classification : 05A18, 05A15, 42C05, 05A30

Byung-Hak Hwang    ; Jang Soo Kim    ; Jaeseong Oh  1   ; Sang-Hoon Yu 

1 Seoul National University 
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     author = {Byung-Hak Hwang and Jang Soo Kim and Jaeseong Oh and Sang-Hoon  Yu},
     title = {On linearization coefficients of {\(q\)-Laguerre} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/9275},
     zbl = {1481.05014},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/9275/}
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Byung-Hak Hwang; Jang Soo Kim; Jaeseong Oh; Sang-Hoon  Yu. On linearization coefficients of \(q\)-Laguerre polynomials. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/9275

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