- Hacettepe Journal of Mathematics and Statistics
- Vol: 44 Issue: 4
- The frobenius problem for some numerical semigroups with embedding dimension equal to three
The frobenius problem for some numerical semigroups with embedding dimension equal to three
Authors : Aureliano M. Robles-pérez, José Carlos Rosales
Pages : 901-908
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Publication Date : 2015-08-01
Article Type : Research
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