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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Popis
Shrnutí: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.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.6366