Cyclotomic numerical semigroup polynomials with at most two irreducible factors

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 $S.$

15 pages

References in corpus (2)

• numericalsgps, a GAP package for numerical semigroups
• Graded algebras with cyclotomic Hilbert series