Cyclotomic numerical semigroup polynomials with at most two irreducible factors.

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 ℓ (S) of S. We show that a cyclotomic numerical semigroup is complete intersection if ℓ (S) ≤ 2 . This establishes a particular case of a conjecture of Ciolan et al. (SIAM J Discrete Math 30(2):650–668, 2016) claiming that every cyclotomic numerical semigroup is complete intersection. In addition, we investigate the relation between ℓ (S) and the embedding dimension of S. [ABSTRACT FROM AUTHOR]