Author:
Borzì Alessio,Herrera-Poyatos Andrés,Moree Pieter
Abstract
AbstractA numerical semigroup S is cyclotomic if its semigroup polynomial $$\mathrm {P}_S$$
P
S
is a product of cyclotomic polynomials. The number of irreducible factors of $$\mathrm {P}_S$$
P
S
(with multiplicity) is the polynomial length $$\ell (S)$$
ℓ
(
S
)
of S. We show that a cyclotomic numerical semigroup is complete intersection if $$\ell (S)\le 2$$
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 $$\ell (S)$$
ℓ
(
S
)
and the embedding dimension of S.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
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