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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Bibliographic Details
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
Online Access:	Get full text
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Summary:	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