On parametrized families of numerical semigroups
On parametrized families of numerical semigroups
A numerical semigroup is an additive subsemigroup of the non-negative integers. In this article, we consider parametrized families of numerical semigroups of the form Pn=〈f1(n),…,fk(n)〉 for polynomial functions fi. We conjecture that for large n, the Betti numbers, Frobenius number, genus, and type of Pn each coincide with a quasipolynomial. …