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.