Staircase skew Schur functions are Schur P-positive
Combinatorics
2011-08-11 v1 Representation Theory
Abstract
We prove Stanley's conjecture that, if delta_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.
Keywords
Cite
@article{arxiv.1108.2219,
title = {Staircase skew Schur functions are Schur P-positive},
author = {Federico Ardila and Luis G. Serrano},
journal= {arXiv preprint arXiv:1108.2219},
year = {2011}
}
Comments
13 pages