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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Published in:Discrete mathematics and theoretical computer science Vol. DMTCS Proceedings, 28th...
Main Author: Roberts, Austin
Format: Journal Article Conference Proceeding
Language:English
Published: DMTCS 22.04.2020
Discrete Mathematics & Theoretical Computer Science
Subjects:
[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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