Title
A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials
Abbreviated Journal Title
Adv. Appl. Math.
Keywords
2D-Hermite polynomials; 2D-Laguerre polynomials; Kibble-Slepian formula; Linearization coefficients; Elementary symmetric functions; Inequalities; Positivity; Shifted Laguerre polynomials; HERMITE-POLYNOMIALS; Mathematics, Applied
Abstract
The first author has recently proved a Kibble-Slepian type formula for the 2D-Hermite polynomials {H-m,H- n(z, (z) over bar)} which extends the Poisson kernel for these polynomials. We provide a combinatorial proof of a closely related formula. The combinatorial structures involved are the so-called m-involutionary l-graphs. They are enumerated in two different manners: first globally, then as the exponential of their connected components. We also give a combinatorial model for the 2D-Laguerre polynomials and study their linearization coefficients. (C) 2014 Elsevier Inc. All rights reserved.
Journal Title
Advances in Applied Mathematics
Volume
64
Publication Date
1-1-2015
Document Type
Article
Language
English
First Page
70
Last Page
88
WOS Identifier
ISSN
0196-8858
Recommended Citation
"A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials" (2015). Faculty Bibliography 2010s. 6596.
https://stars.library.ucf.edu/facultybib2010/6596
Comments
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