Staircase skew Schur functions are Schur P-positive

Authors:
Federico Ardila;Luis G. Serrano
Affiliations:
Department of Mathematics, San Francisco State University, San Francisco, USA;LaCIM, Université du Québec à Montréal, Montréal, Canada
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2012

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Abstract

We prove Stanley's conjecture that, if 驴 n is the staircase shape, then the skew Schur functions $s_{\delta_{n} / \mu}$ are non-negative sums of Schur P-functions. We prove that the coefficients in this sum count certain fillings of shifted shapes. In particular, for the skew Schur function $s_{\delta_{n} / \delta _{n-2}}$ , we discuss connections with Eulerian numbers and alternating permutations.