Möbius function of semigroup posets through Hilbert series

Autor: Jorge Luis Ramírez Alfonsín, Jonathan Chappelon, Luis Pedro Montejano, Ignacio García-Marco
Přispěvatelé: Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)
Jazyk: angličtina
Rok vydání: 2015
Předmět:
Hilbert series
0102 computer and information sciences
Characterization (mathematics)
Möbius function
01 natural sciences
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
Theoretical Computer Science
Combinatorics
symbols.namesake
Locally finite poset
[MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
Discrete Mathematics and Combinatorics
Mathematics - Combinatorics
0101 mathematics
Mathematics
Hilbert–Poincaré series
2010MSC : 20M15
05A99
06A07
11A25
20M05
20M25
Mathematics::Combinatorics
Mathematics - Number Theory
Semigroup
Mathematics::Operator Algebras
locally finite poset
010102 general mathematics
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Graded poset
Computational Theory and Mathematics
010201 computation theory & mathematics
denumerant
semigroup
symbols
Partially ordered set
Mathematics - Group Theory
Zdroj: Journal of Combinatorial Theory, Series A
Journal of Combinatorial Theory, Series A, Elsevier, 2015, 136, pp.238-251. ⟨10.1016/j.jcta.2015.07.006⟩
ISSN: 0097-3165
1096-0899
DOI: 10.1016/j.jcta.2015.07.006⟩
Popis: In this paper, we investigate the M{\"o}bius function $\mu\_{\mathcal{S}}$ associated to a (locally finite) poset arising from a semigroup $\mathcal{S}$ of $\mathbb{Z}^m$. We introduce and develop a new approach to study $\mu\_{\mathcal{S}}$ by using the Hilbert series of $\mathcal{S}$. The latter enables us to provide formulas for $\mu\_{\mathcal{S}}$ when $\mathcal{S}$ belongs to certain families of semigroups. Finally, a characterization for a locally finite poset to be isomorphic to a semigroup poset is given.
Comment: 11 pages
Databáze: OpenAIRE
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