The frobenius problem for some numerical semigroups with embedding dimension equal to three

Authors : Aureliano M ROBLESPÉREZ, José Carlos ROSALES

Pages : 901-908

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Publication Date : 2015-08-01

Article Type : Research Paper

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 gcdinsert ignore into journalissuearticles values( a, b ); = gcdinsert ignore into journalissuearticles values( a,c ); = gcdinsert ignore into journalissuearticles values( 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