4 research outputs found
M\"obius function of semigroup posets through Hilbert series
In this paper, we investigate the M{\"o}bius function
associated to a (locally finite) poset arising from a semigroup
of . We introduce and develop a new approach to study
by using the Hilbert series of . The latter
enables us to provide formulas for when
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 page
Chomp on numerical semigroups
We consider the two-player game chomp on posets associated to numerical
semigroups and show that the analysis of strategies for chomp is strongly
related to classical properties of semigroups. We characterize, which player
has a winning-strategy for symmetric semigroups, semigroups of maximal
embedding dimension and several families of numerical semigroups generated by
arithmetic sequences. Furthermore, we show that which player wins on a given
numerical semigroup is a decidable question. Finally, we extend several of our
results to the more general setting of subsemigroups of ,
where is a finite abelian group.Comment: 22 pages, 14 figures, 1 table (improved exposition