Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number

Abstract

A C-semigroup (respectively a D-semigroup) is a positioned numerical semigroup S such that g(S)=F(S)+m(S)−12 (respectively g(S)=F(S)+m(S)−22). In this paper we study these semigroups giving formulas for the Frobenius number, pseudo-Frobenius number, and type. Furthermore, we give algorithms for computing the whole set of C-semigroups and D-semigroups.