The Frobenius problem for numerical semigroups with embedding dimension equal to three
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- by Aureliano M. Robles-Pérez and José Carlos Rosales;
- Math. Comp. 81 (2012), 1609-1617
- DOI: https://doi.org/10.1090/S0025-5718-2011-02561-5
- 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.References
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Bibliographic 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
- 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.
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 1609-1617
- MSC (2010): Primary 11D07, 20M14
- DOI: https://doi.org/10.1090/S0025-5718-2011-02561-5
- MathSciNet review: 2904593