The Frobenius problem for numerical semi-groups

Abstract

In this paper, we characterize those numerical semigroups containing hn1, n2i. 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.