Some results on the Frobenius coin problem

Abstract

The Frobenius coin problem consists in finding a formula, in terms of the elements in a minimal system of generators of a numerical semigroup, for computing the Frobenius number and the genus. In this paper we will present some classes of numerical semigroups for which this problem is solved. We give formulas for the Frobenius number, type and the genus for MED-semigroups, Mersenne numerical semigroups, Thabit numerical semigroups, Repunit numerical semigroups and numerical semigroups with multiplicity four.