Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 11 (2015), 039, 12 pages      arXiv:1501.03880      https://doi.org/10.3842/SIGMA.2015.039
Contribution to the Special Issue on Exact Solvability and Symmetry Avatars in honour of Luc Vinet

The Combinatorics of Associated Laguerre Polynomials

Jang Soo Kim a and Dennis Stanton b
a) Department of Mathematics, Sungkyunkwan University, Suwon 440-746, South Korea
b) School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Received January 30, 2015, in final form May 06, 2015; Published online May 11, 2015

Abstract
The explicit double sum for the associated Laguerre polynomials is derived combinatorially. The moments are described using certain statistics on permutations and permutation tableaux. Another derivation of the double sum is provided using only the moment generating function.

Key words: associated Laguerre polynomial; moment of orthogonal polynomials, permutation tableau.

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