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Numerical semigroups with a given set of pseudo-Frobenius numbers

Part of: Semigroups Diophantine equations

Published online by Cambridge University Press:  01 April 2016

M. Delgado ,
P. A. García-Sánchez  and
A. M. Robles-Pérez
M. Delgado
Affiliation:
CMUP, Departamento de Matemática, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal email mdelgado@fc.up.pt
P. A. García-Sánchez
Affiliation:
IEMath-GR, Departamento de Álgebra, Universidad de Granada, 18071 Granada, Spain email pedro@ugr.es
A. M. Robles-Pérez
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain email arobles@ugr.es

Abstract

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The pseudo-Frobenius numbers of a numerical semigroup are those gaps of the numerical semigroup that are maximal for the partial order induced by the semigroup. We present a procedure to detect if a given set of integers is the set of pseudo-Frobenius numbers of a numerical semigroup and, if so, to compute the set of all numerical semigroups having this set as set of pseudo-Frobenius numbers.

MSC classification

Primary: 11D07: The Frobenius problem 20M14: Commutative semigroups

Information

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 186 - 205
Copyright
© The Author(s) 2016 

References

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