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arXiv · 2101.08823

Cyclotomic numerical semigroup polynomials with at most two irreducible factors

Alessio Borzì·Andrés Herrera-Poyatos·Pieter Moree
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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, 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 $S.$

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Alessio Borzì, Andrés Herrera-Poyatos, Pieter Moree. 2021-01-21. Cyclotomic numerical semigroup polynomials with at most two irreducible factors. https://doi.org/10.1007/s00233-021-10197-8

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