Geodesic
Staircase skew Schur functions are Schur $P$-positive
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 409-423.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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: Schur functions, Schur P-functions, shifted tableaux, Eulerian numbers, alternating permutations 
@article{JAC_2012__36_3_a3,
     author = {Ardila, Federico and Serrano, Luis G.},
     title = {Staircase skew {Schur} functions are {Schur} $P$-positive},
     journal = {Journal of Algebraic Combinatorics},
     pages = {409--423},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a3/}
}
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Ardila, Federico; Serrano, Luis G. Staircase skew Schur functions are Schur $P$-positive. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 3, pp. 409-423. http://geodesic.mathdoc.fr/item/JAC_2012__36_3_a3/