Numerical semigroups without consecutive small elements.

Abstract

In this work, we study A-semigroups, that is, numerical semigroups which have no consecutive elements less than the Frobenius number. We give algorithms that allow computation of the whole set of A-semigroups with a given genus, multiplicity and Frobenius number and from this we study interesting families of A-semigroups which are Frobenius varieties, pseudo-varieties; R-varieties.