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Cyclotomic numerical semigroup polynomials with at most two irreducible factors
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Borzì, Alessio, Herrera-Poyatos, Andrés and Moree, Pieter (2021) Cyclotomic numerical semigroup polynomials with at most two irreducible factors. Semigroup Forum, 103 (3). pp. 812-828. doi:10.1007/s00233-021-10197-8 ISSN 1432-2137.
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Official URL: https://doi.org/10.1007/s00233-021-10197-8
Abstract
A numerical semigroup S is cyclotomic if its semigroup polynomial PS is a product of cyclotomic polynomials. The number of irreducible factors of PS (with multiplicity) is the polynomial length ℓ(S) of S. We show that a cyclotomic numerical semigroup is complete intersection if ℓ(S)≤2. This establishes a particular case of a conjecture of Ciolan et al. (SIAM J Discrete Math 30(2):650–668, 2016) claiming that every cyclotomic numerical semigroup is complete intersection. In addition, we investigate the relation between ℓ(S) and the embedding dimension of S.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| SWORD Depositor: | Library Publications Router | ||||||||
| Library of Congress Subject Headings (LCSH): | Semigroups, Polynomials, Cyclotomy | ||||||||
| Journal or Publication Title: | Semigroup Forum | ||||||||
| Publisher: | Springer US | ||||||||
| ISSN: | 1432-2137 | ||||||||
| Official Date: | December 2021 | ||||||||
| Dates: |
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| Volume: | 103 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 812-828 | ||||||||
| DOI: | 10.1007/s00233-021-10197-8 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 19 July 2023 | ||||||||
| Date of first compliant Open Access: | 19 July 2023 | ||||||||
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