Staircase skew Schur functions are Schur P-positive

Details Staircase skew Schur functions are Schur P-positive Staircase skew Schur functions are Schur P-positive

2011-08-10

arxiv.org/abs/1108.2219v1

Mathematics

Combinatorics

13 pages

Scientific paper

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.

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