The frobenius problem for some 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 = ⟨a, b, cb − da⟩ with a, b, c, d positive integers such that gcd(a, b) = gcd(a,c) = gcd(b,d) = 1, c ∈ {2,...,a−1}, and a < b < cb−da. In this paper we give formulas, in terms of a, b, c, d, for the genus, the Frobenius number, and the set of pseudo-Frobenius numbers of ⟨a, b, cb − da⟩ in the case in which the interval $[a/c, b/d]$ contains some integer. 

Keywords

• Frobenius problem,numerical semigroups,Apéry set

References

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