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Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2020

Symmetric Fundamental Expansions to Schur Positivity

Abstract

We consider families of quasisymmetric functions with the property that if a symmetric function f is a positive sum of functions in one of these families, then f is necessarily a positive sum of Schur functions. Furthermore, in each of the families studied, we give a combinatorial description of the Schur coefficients of f. We organize six such families into a poset, where functions in higher families in the poset are always positive integer sums of functions in each of the lower families.

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Dates and versions

hal-02166335 , version 1 (26-06-2019)

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Austin Roberts. Symmetric Fundamental Expansions to Schur Positivity. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6366⟩. ⟨hal-02166335⟩
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