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Schur-positivity via products of grid classes

Abstract : Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur- positive is a long-standing problem in algebraic combinatorics. In this paper we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets, and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.
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Submitted on : Thursday, July 4, 2019 - 2:23:47 PM
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Sergi Elizalde, Yuval Roichman. Schur-positivity via products of grid classes. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨hal-02173379⟩

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