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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The Frobenius problem for numerical semigroups with embedding dimension equal to three


Authors: Aureliano M. Robles-Pérez and José Carlos Rosales
Journal: Math. Comp. 81 (2012), 1609-1617
MSC (2010): Primary 11D07, 20M14
Published electronically: November 3, 2011
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Abstract: Let $ S$ be a numerical semigroup with embedding dimension equal to three. Assume that the minimal generators of $ S$ are pairwise relatively prime numbers. Under these conditions, we give semi-explicit formulas for the Frobenius number, the genus, and the set of pseudo-Frobenius numbers of $ S$. Moreover, if the multiplicity of $ S$ is fixed, then these formulas become explicit.


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Additional Information

Aureliano M. Robles-Pérez
Affiliation: Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: arobles@ugr.es

José Carlos Rosales
Affiliation: Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071-Granada, Spain
Email: jrosales@ugr.es

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02561-5
PII: S 0025-5718(2011)02561-5
Keywords: Frobenius problem, numerical semigroups, multiplicity
Received by editor(s): October 27, 2010
Received by editor(s) in revised form: March 22, 2011
Published electronically: November 3, 2011
Additional Notes: Both authors were supported by MTM2007-62346 (MEC, Spain), MTM2010-15595 (MICINN, Spain) and FEDER funds.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.