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math.CO2011
The down operator and expansions of near rectangular k-Schur functions
Chris Berg, Franco Saliola, Luis Serrano
We prove that the Lam-Shimozono "down operator" on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this t…
math.CO2011
Staircase skew Schur functions are Schur P-positive
Federico Ardila, Luis G. Serrano
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…