A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials

    Authors

    M. E. H. Ismail;J. Zeng

    Comments

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    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

    WOS:000348883400005

    ISSN

    0196-8858

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