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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Vydáno v:	Discrete mathematics and theoretical computer science Ročník DMTCS Proceedings, 28th...
Hlavní autor:	White, Jacob
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
ISSN:	1365-8050, 1462-7264, 1365-8050
On-line přístup:	Získat plný text
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Popis
Shrnutí:	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