Borzì, Alessio and Herrera-Poyatos, Andrés and Moree, Pieter (2021) Cyclotomic numerical semigroup polynomials with few irreducible factors. MPIM Preprint Series 2021 (6).
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Abstract
A numerical semigroup $S$ is cyclotomic if its semigroup polynomial $P_S$ is a product of cyclotomic polynomials. The number of irreducible factors of $P_S$ (with multiplicity) is the polynomial length $\ell(S)$ of $S.$
We show that a cyclotomic numerical semigroup is complete intersection if $\ell(S)\le 2$. This establishes a particular case of a conjecture of Ciolan, García-Sánchez and Moree (2016) claiming that every cyclotomic numerical semigroup is complete intersection. In addition, we investigate the relation between $\ell(S)$ and the embedding dimension of $S.$
| Item Type: | MPIM Preprint |
|---|---|
| Subjects: | 1 Discrete mathematics / algebra > 20-XX Group theory and generalizations |
| Divisions: | Research > Preprints |
| Depositing User: | Andrea Kohlhuber |
| Date Deposited: | 11 Feb 2021 11:47 |
| Last Modified: | 11 Feb 2021 11:48 |
| URI: | https://archive.mpim-bonn.mpg.de/id/eprint/4199 |
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