Arf numerical semigroups with multiplicity 11 and 13

Abstract

Parametrizations are given for Arf numerical semigroups with multiplicity up to 10. In this work, we give parametrizations of Arf numerical semigroups with multiplicity 11 and 13, and combining these results with previous results about the number of Arf numerical semigroups with multiplicity 2, 3, 5, 7, we share some observations about the set of Arf numerical semigroups with prime multiplicity.