2 research outputs found
Cyclotomic exponent sequences of numerical semigroups
We study the cyclotomic exponent sequence of a numerical semigroup and we compute its values at the gaps of the elements of with unique representations in terms of minimal generators, and the Betti elements for which the set is totally ordered with respect to (we write whenever with ). This allows us to characterize certain semigroup families, such as Betti-sorted or Betti-divisible numerical semigroups, as well as numerical semigroups with a unique Betti element, in terms of their cyclotomic exponent sequences. Our results also apply to cyclotomic numerical semigroups, which are numerical semigroups with a finitely supported cyclotomic exponent sequence. We show that cyclotomic numerical semigroups with certain cyclotomic exponent sequences are complete intersections, thereby making progress towards proving the conjecture of Ciolan, García-Sánchez and Moree (2016) stating that is cyclotomic if and only if it is a complete intersection