Factorizations of the same length in abelian monoids

  1. García Barroso, Evelia R.
  2. García-Marco, Ignacio
  3. Márquez-Corbella, Irene
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

Zeitschrift:
Ricerche di Matematica

ISSN: 0035-5038,  1827-3491

Datum der Publikation: 2023

Ausgabe: 72

Seiten: 679-707

Art: Artikel

DOI: 10.1007/S11587-021-00562-8 GOOGLE SCHOLAR

Andere Publikationen in: Ricerche di Matematica

Zusammenfassung

Let S⊆Zm⊕T be a finitely generated and reduced monoid. In this paper we develop a general strategy to study the set of elements in S having at least two factorizations of the same length, namely the ideal LS. To this end, we work with a certain (lattice) ideal associated to the monoid S. Our study can be seen as a new approach generalizing [9], which only studies the case of numerical semigroups. When S is a numerical semigroup we give three main results: (1) we compute explicitly a set of generators of the ideal LS when S is minimally generated by an almost arithmetic sequence; (2) we provide an infinite family of numerical semigroups such that LS is a principal ideal; (3) we classify the computational problem of determining the largest integer not in LS as an NP-hard problem.

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