Cyclotomic numerical semigroup polynomials with at most two irreducible factors
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 (S) of S. We show that a cyclotomic numerical semigroup is complete intersection if (S) 2. This establishes a particular case of a conjecture of Ciolan, Garc\'ia-S\'anchez and Moree (2016) claiming that every cyclotomic numerical semigroup is complete intersection. In addition, we investigate the relation between (S) and the embedding dimension of S.
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