Jacobi-Stirling polynomials and P-partitions

Authors:
Ira M. Gessel;Zhicong Lin;Jiang Zeng
Affiliations:
Department of Mathematics, Brandeis University, Waltham, MA 02453-2728, USA;Department of Mathematics and Statistics, Lanzhou University, China and Université/ de Lyon/ Université/ Lyon 1/ Institut Camille Jordan/ UMR 5208 du CNRS/ 43, boulevard du 11 novembre 191 ...;Université/ de Lyon/ Université/ Lyon 1/ Institut Camille Jordan/ UMR 5208 du CNRS/ 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
Venue:
European Journal of Combinatorics
Year:
2012

Citing 6
Cited 1

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Abstract

We investigate the diagonal generating function of the Jacobi-Stirling numbers of the second kind JS(n+k,n;z) by generalizing the analogous results for the Stirling and Legendre-Stirling numbers. More precisely, letting JS(n+k,n;z)=p"k","0(n)+p"k","1(n)z+...+p"k","k(n)z^k, we show that (1-t)^3^k^-^i^+^1@?"n"="0p"k","i(n)t^n is a polynomial in t with nonnegative integral coefficients and provide combinatorial interpretations of the coefficients by using Stanley's theory of P-partitions.