The Combinatorics of Associated Laguerre Polynomials
Jang Soo Kim, Dennis Stanton
TL;DR
This paper derives a combinatorial explicit double sum for associated Laguerre polynomials, relates moments to permutation statistics, and offers an alternative derivation using the moment generating function.
Contribution
It provides a new combinatorial explicit formula and a novel derivation method for associated Laguerre polynomials and their moments.
Findings
Explicit double sum formula for associated Laguerre polynomials
Moments described via permutation statistics
Alternative derivation using moment generating function
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.
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