The Frobenius problem for numerical semigroups with embedding dimension equal to three

Abstract

If S is a numerical semigroup with embedding dimension equal to three whose minimal generators are pairwise relatively prime numbers, then S =ha;b;cb dai with a;b;c;d positive integers such that gcd(a;b) = gcd(a;c) = gcd(b;d) = 1, c2f2;:::;a 1g, anda < b < cb da. In this paper we give formulas, in terms ofa;b;c;d, for the genus, the Frobenius number, and the set of pseudo-Frobenius numbers ofha;b;cb dai in the case in which the interval a ; b d contains some integer.