The set of numerical semigroups of a given multiplicity and Frobenius number

Abstract

We study the structure of the family of numerical semigroups with fixed multiplicity and Frobenius number. We give an algorithmic method to compute all the semigroups in this family. Moreover, several characterizations of this family are given. As an application we compute the set of all numerical semigroups with given multipliciy and gender.

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Manuel B. Branco, Ignacio Ojeda, José Carlos Rosales, The set of numerical semigroups of a given multiplicity and Frobenius number. Port. Math. 78 (2021), no. 2, pp. 147–167

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