English

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}
}

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13 pages