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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
Posted:
November 3, 2011
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Abstract |
References |
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Additional Information
Abstract: Let  be a numerical semigroup with embedding dimension equal to three. Assume that the minimal generators of  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  . Moreover, if the multiplicity of  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
Posted:
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 after
28 years from publication.
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