Symmetric Fundamental Expansions to Schur Positivity

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...

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Vydáno v:Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autor: Roberts, Austin
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Témata:
[math.math-co]mathematics [math]/combinatorics [math.co]
Combinatorics
Mathematics
Combinatorics
ISSN:1365-8050, 1462-7264, 1365-8050
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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.
AbstractList 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.
Author Roberts, Austin
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Combinatorics
Mathematics
Title Symmetric Fundamental Expansions to Schur Positivity
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