Parametrizing numerical semigroups with multiplicity up to 5

Abstract

In this work, we give parametrizations in terms of the Kunz coordinates of numerical semigroups with multiplicity up to 5. We also obtain parametrizations of MED semigroups, symmetric and pseudo-symmetric numerical semigroups with multiplicity up to 5. These parametrizations also lead to formulas for the number of numerical semigroups, the number of MED semigroups and the number of symmetric and pseudo-symmetric numerical semigroups with multiplicity up to 5 and given conductor. © 2018 World Scientific Publishing Company.