Legendre-Stirling permutations

Authors:
Eric S. Egge
Affiliations:
Department of Mathematics, Carleton College, Northfield, MN 55057, USA
Venue:
European Journal of Combinatorics
Year:
2010

Citing 4
Cited 4

Two notes on notation

American Mathematical Monthly
Legendre polynomials, Legendre--Stirling numbers, and the left-definite spectral analysis of the Legendre differential expression

Journal of Computational and Applied Mathematics - On the occasion of the 65th birthday of Prof. Michael Eastham
Generatingfunctionology

Generatingfunctionology
Real Zeros and Normal Distribution for Statistics on Stirling Permutations Defined by Gessel and Stanley

SIAM Journal on Discrete Mathematics

Stable multivariate Eulerian polynomials and generalized Stirling permutations

European Journal of Combinatorics
Jacobi-Stirling polynomials and P-partitions

European Journal of Combinatorics
The Jacobi-Stirling numbers

Journal of Combinatorial Theory Series A
Stirling permutations on multisets

European Journal of Combinatorics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We first give a combinatorial interpretation of Everitt, Littlejohn, and Wellman's Legendre-Stirling numbers of the first kind. We then give a combinatorial interpretation of the coefficients of the polynomial (1-x)^3^k^+^1@?"n"="0^~{{n+kn}}x^n analogous to that of the Eulerian numbers, where {{nk}}are Everitt, Littlejohn, and Wellman's Legendre-Stirling numbers of the second kind. Finally we use a result of Bender to show that the limiting distribution of these coefficients as n approaches infinity is the normal distribution.