Multilinear generating functions for Charlier polynomials
Ira M. Gessel, Pallavi Jayawant
TL;DR
This paper presents a combinatorial proof of a multilinear generating function for Charlier polynomials, connecting it to derangements and bilinear generating functions, thus enriching the combinatorial understanding of these polynomials.
Contribution
It introduces a new combinatorial proof for the multilinear generating function of Charlier polynomials using Charlier configurations.
Findings
Derived a multilinear generating function for Charlier polynomials
Obtained bilinear generating functions as special cases
Provided formulas related to derangements
Abstract
Charlier configurations provide a combinatorial model for Charlier polynomials. We use this model to give a combinatorial proof of a multilinear generating function for Charlier polynomials. As special cases of the multilinear generating function, we obtain the bilinear generating function for Charlier polynomials and formulas for derangements.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Advanced Mathematical Identities