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The genus, Frobenius number and pseudo-Frobenius numbers of numerical semigroups of type 2

Part of: Local rings and semilocal rings Diophantine equations Semigroups

Published online by Cambridge University Press:  19 July 2016

Aureliano M. Robles-Pérez  and
José Carlos Rosales
Aureliano M. Robles-Pérez
Affiliation:
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain (arobles@ugr.es)
José Carlos Rosales
Affiliation:
Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain (jrosales@ugr.es)
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Extract

We study some questions on numerical semigroups of type 2. On the one hand, we investigate the relation between the genus and the Frobenius number. On the other hand, for two fixed positive integers g1, g2, we give necessary and sufficient conditions in order to have a numerical semigroup S such that {g1, g2} is the set of its pseudo-Frobenius numbers and, moreover, we explicitly build families of such numerical semigroups.

Keywords

Frobenius numberpseudo-Frobenius numbernumerical semigroupsgenustype

MSC classification

Secondary: 11D07: The Frobenius problem 20M14: Commutative semigroups 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 5 , October 2016 , pp. 1081 - 1090
Copyright
Copyright © Royal Society of Edinburgh 2016 

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