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

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

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 pseu...

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on numerical semigroups with embedding dimension three

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On Numerical Semigroups with Embedding Dimension Three

Let f ̸= 1, 3 be a positive integer. We prove that there exists a numerical semigroup S with embedding dimension three such that f is the Frobenius number of S. We also show that the same fact holds for affine semigroups in higher dimensional monoids.

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Factoring in Embedding Dimension Three Numerical Semigroups

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ژورنال

عنوان ژورنال: Mathematics of Computation

سال: 2012

ISSN: 0025-5718,1088-6842

DOI: 10.1090/s0025-5718-2011-02561-5