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Cyclotomic exponent sequences of numerical semigroups
dc.contributor.author | Ciolan, Alexandru | |
dc.contributor.author | García Sánchez, Pedro Abelardo | |
dc.contributor.author | Herrera-Poyatos, Andrés | |
dc.contributor.author | Moree, Pieter | |
dc.date.accessioned | 2022-02-21T12:03:21Z | |
dc.date.available | 2022-02-21T12:03:21Z | |
dc.date.issued | 2021-01-21 | |
dc.identifier.citation | Publisher version: A. Ciolan, P.A. García-Sánchez, A. Herrera-Poyatos et al. Cyclotomic exponent sequences of numerical semigroups. Discrete Mathematics 345 (2022) 112820 [https://doi.org/10.1016/j.disc.2022.112820] | es_ES |
dc.identifier.uri | http://hdl.handle.net/10481/72926 | |
dc.description | Part of the work on this paper was done during an internship in the Fall of 2016 carried out by the third author at the Max Planck Institute for Mathematics in Bonn and during a one-week visit in April 2019. He would like to thank the fourth author for the invitation and the institute staff for their hospitality and support. The project was completed during a stay of the first author at the same institute. Substantial progress on this paper was made in February 2017, when the first and the fourth author were invited by the second and third author for one week to the University of Granada. They are grateful for the hospitality, for the inspiring and cheerful atmosphere and, last but not least, for the excellent tapas and wine! | es_ES |
dc.description.abstract | We study the cyclotomic exponent sequence of a numerical semigroup S, and we compute its values at the gaps of S, the elements of S with unique representations in terms of minimal generators, and the Betti elements b∈S for which the set {a∈Betti(S):a≤Sb} is totally ordered with respect to ≤S (we write a≤Sb whenever a−b∈S, with a,b∈S). This allows us to characterize certain semigroup families, such as Betti-sorted or Betti-divisible numerical semigroups, as well as numerical semigroups with a unique Betti element, in terms of their cyclotomic exponent sequences. Our results also apply to cyclotomic numerical semigroups, which are numerical semigroups with a finitely supported cyclotomic exponent sequence. We show that cyclotomic numerical semigroups with certain cyclotomic exponent sequences are complete intersections, thereby making progress towards proving the conjecture of Ciolan, García-Sánchez and Moree (2016) stating that S is cyclotomic if and only if it is a complete intersection. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Elsevier | es_ES |
dc.rights | Atribución-NoComercial-SinDerivadas 3.0 España | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.title | Cyclotomic exponent sequences of numerical semigroups | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es_ES |
dc.identifier.doi | 10.1016/j.disc.2022.112820 | |
dc.type.hasVersion | info:eu-repo/semantics/submittedVersion | es_ES |