The Frobenius problem for numerical semigroups

Abstract

In this paper, we characterize those numerical semigroups containing n1,n2 . From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators.