On the weight of numerical semigroups

Abstract

a b s t r a c tWe investigate the weights of a family of numerical semigroups by means of even gaps and the Weierstrass property for such a family.

The proportion of Weierstrass semigroups

“…There are other known examples of semigroups which are known to be Weierstrass but do not fit into this Eisenbud and Harris family, and semigroups which are not Weierstrass but do not fail the Buchweitz criterion. See for example [13,14].…”

Counting numerical semigroups by genus and even gaps

“…[32]) we point out a quite useful parametrization, namely S γ (g) → S γ , S → S/2, which was introduced by Rosales et al [29] (see (2.3), [28], [17]). Thus Remark 2.11 shows the class of numerical semigroups we deal with in this paper; we do observe that these semigroups were already studied for example in [25] by using the concept of weight of semigroups.…”

$K$-weight bounds for $γ$-hyperelliptic semigroups

“…Finally, just as in [4], it is natural to ask for refinements of Theorem 2.1. We have the following K-weight analogue of [4, Props.…”