Cyclotomic numerical semigroup polynomials with at most two irreducible factors

Borzì, Alessio; Herrera-Poyatos, Andrés; Moree, Pieter

doi:10.1007/s00233-021-10197-8

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Cyclotomic numerical semigroup polynomials with at most two irreducible factors

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Moree, Pieter
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00233-021-10197-8
(Publisher version)

https://doi.org/10.48550/arXiv.2101.08823
(Preprint)

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Borzi-Herrera-Poyaros-Moree_Cyclotomic numerical semigroup polynomials with at most two irreducible factors_2021.pdf
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Citation

Borzì, A., Herrera-Poyatos, A., & Moree, P. (2021). Cyclotomic numerical semigroup polynomials with at most two irreducible factors. Semigroup forum, 103(3), 812-828. doi:10.1007/s00233-021-10197-8.

Cite as: https://hdl.handle.net/21.11116/0000-0008-A7E7-7

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, Garc\'{i}a-S\'{a}nchez
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 $S.$