Positioned Numerical Semigroups with Small Gender

Abstract

An M-semigroup (respectively an N -semigroup) is a positioned numerical semigroup S, such that g(S) = F(S)+3/2 (respectively, g(S) = F(S)+4/2 ). In this paper, we describe and characterize this class of semigroups; in particular, we show that the type of an M-semigroup (respectively an N-semigroup) is equal to 2 or 3 (respectively 2, 3 or 4). Moreover, we give algorithms for computing the whole set of M-semigroups and N-semigroups.