The combinatorics of associated Hermite polynomials

被引：17
作者：
Drake, Dan [1 ]
机构：
[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Taejon 305701, South Korea
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2009年 / 30卷 / 04期
关键词：
LAGUERRE; IDENTITIES; LINEARIZATION; FILLINGS; BIRTH;
D O I：
10.1016/j.ejc.2008.05.009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected complete matchings, oscillating tableaux, and rooted maps and show weight-preserving bijections between these objects. Several identities, linearization formulas, the moment generating function, and a second combinatorial model are also derived. (C) 2008 Elsevier Ltd. All rights reserved.
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页码：1005 / 1021
页数：17
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