Poincar\'e series of semigroups
Antonio Campillo, Raquel Melgar
TL;DR
This paper provides new explicit formulas for the Poincaré series of finitely generated positive cancellative commutative semigroups, with proofs using combinatorial and topological methods.
Contribution
It introduces several elementary, closed-form formulas for the Poincaré series, connecting algebraic invariants with simplicial complexes and set theory.
Findings
Multiple closed formulas for Poincaré series
Elementary proofs using combinatorial and topological methods
Formulas expressed via simplicial complexes and set theory
Abstract
Many invariants of finitely generated positive cancelative commutative semigroups can be studied from their Poincar\'e series. We offer and present several closed formulas for them. Moreover, those formulas have elementary proofs and are presented in two distinct forms: one characterized in terms of simplicial complexes and the other by a purely set theoretical approach.
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Taxonomy
TopicsFuzzy and Soft Set Theory · semigroups and automata theory