Jang Soo Kim, Dennis Stanton, “The Combinatorics of Associated Laguerre Polynomials”, SIGMA, 2015, Volume 11,039, 12 pp.

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The Combinatorics of Associated Laguerre Polynomials

Jang Soo Kim^a, 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

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.

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

MSC: 05E35; 05A15

Received: January 30, 2015; in final form May 6, 2015; Published online May 11, 2015

Language: English

DOI: 10.3842/SIGMA.2015.039