A COMBINATORIAL INTERPRETATION OF THE LEGENDRE-STIRLING NUMBERS

被引：34

作者：

Andrews, George E. ^{[1
]}

Littlejohn, Lance L. ^{[2
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16801 USA

[2] Baylor Univ, Dept Math, Waco, TX 76798 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 08期

关键词：

Legendre-Stirling numbers; Stirling numbers of the second kind; Legendre polynomials; left-definite theory; self-adjoint operator; POLYNOMIALS;

D O I：

10.1090/S0002-9939-09-09814-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Legendre-Stirling numbers were discovered in 2002 as a result of a problem involving the spectral theory of powers of the classical second-order Legendre differential expression. Specifically, these numbers are the coefficients of integral composite powers of the Legendre expression in Lagrangian symmetric form. Quite remarkably, they share many similar properties with the classical Stirling numbers of the second kind which, as shown by Littlejohn and Wellman, are the coefficients of integral powers of the Laguerrc differential expression. An open question regarding the Legendre-Stirling numbers has been to obtain a combinatorial interpretation of these numbers. In this paper, we provide such an interpretation.

引用

页码：2581 / 2590

页数：10