Quasisymmetric functions from combinatorial Hopf monoids and Ehrhart Theory

We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class of complexes, called forbidden composition compl...

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Veröffentlicht in:	Discrete mathematics and theoretical computer science Jg. DMTCS Proceedings, 28th...
1. Verfasser:	White, Jacob
Format:	Journal Article Tagungsbericht
Sprache:	Englisch
Veröffentlicht:	DMTCS 22.04.2020 Discrete Mathematics & Theoretical Computer Science
Schlagworte:	[math.math-co]mathematics [math]/combinatorics [math.co] Combinatorics Mathematics
ISSN:	1365-8050, 1462-7264, 1365-8050
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We investigate quasisymmetric functions coming from combinatorial Hopf monoids. We show that these invariants arise naturally in Ehrhart theory, and that some of their specializations are Hilbert functions for relative simplicial complexes. This class of complexes, called forbidden composition complexes, also forms a Hopf monoid, thus demonstrating a link between Hopf algebras, Ehrhart theory, and commutative algebra. We also study various specializations of quasisymmetric functions.
ISSN:	1365-8050 1462-7264 1365-8050
DOI:	10.46298/dmtcs.6334