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

Robles-Pérez, Aureliano; Rosales, José

doi:10.1090/S0025-5718-2011-02561-5

The Frobenius problem for numerical semigroups with embedding dimension equal to three
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by Aureliano M. Robles-Pérez and José Carlos Rosales PDF

Math. Comp. 81 (2012), 1609-1617 Request permission

Abstract:

Let $S$ be a numerical semigroup with embedding dimension equal to three. Assume that the minimal generators of $S$ are pairwise relatively prime numbers. Under these conditions, we give semi-explicit formulas for the Frobenius number, the genus, and the set of pseudo-Frobenius numbers of $S$. Moreover, if the multiplicity of $S$ is fixed, then these formulas become explicit.

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