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The arithmetic extensions of a numerical semigroup (2003.05193v2)
Published 11 Mar 2020 in math.AC and math.GR
Abstract: In this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained.
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