RF-Matrices of Arf Numerical Semigroups With Small Multiplicity
DOI:
https://doi.org/10.26713/cma.v14i2.2126Keywords:
ARF numerical semigroups, Frobenius number, Pseudo-Frobenius number, Multiplicity, RF-matricesAbstract
In this paper, multiplicity of Arf numerical semigroups and RF-matrices are given. We study Arf numerical semigroups with multiplicity of two, three, four, five and six with RF-matrices.
Downloads
References
C. Arf, Une interprétation algébrique de la suite des ordres de multiplicité d’une branche algébrique, Proceedings of the London Mathematical Society s2-50(1 (1945)), 256 – 287, DOI: 10.1112/plms/s2-50.4.256.
A. Assi and P. A. García-Sánchez, Numerical Semigroups and Applications, 1st edition, RSME Springer Series, Springer Cham, xiv + 106 pages (2016), DOI: 10.1007/978-3-319-41330-3.
V. Barucci, D. E. Dobbs and M. Fontana, Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains, Memoirs of the American Mathematical Society 125(598), x + 78 pages (1997), DOI: 10.1090/memo/0598.
A. Campillo, J. I. Farran and C. Munuera, On the parameters of algebraic-geometry codes related to Arf semigroups, IEEE Transactions on Information Theory 46(7) (2000), 2634 – 2638, DOI: 10.1109/18.887872.
P. Du Val, The Jacobian algorithm and the multiplicity sequence of an algebraic branch, Revue de la faculte des sciences de l’universite d’Istanbul, Serie A VII (1942), 107 – 112.
GAP Group, GAP — Groups, Algorithms, Programming – a System for Computational Discrete Algebra, Version 4.7.8, The GAP Group (2014), URL: http://www.gap-system.org, accessed December, 2022.
P. A. García-Sánchez, B. A. Heredia, H. ˙I. Karaka¸s and J. C. Rosales, Parametrizing Arf numerical semigroups, Journal of Algebra and Its Applications 16(11) (2017), 1750209, DOI: 10.1142/S0219498817502097.
J. Herzog and K.-I. Watanabe, Almost symmetric numerical semigroups, Semigroup Forum 98 (2019), 589 – 630, DOI: 10.1007/s00233-019-10007-2.
J. Lipman, Stable ideals and Arf rings, American Journal of Mathematics 93(3) (1971), 649 – 685, DOI: 10.2307/2373463.
J. C. Rosales and M. B. Branco, The Frobenius problem for numerical semigroups with multiplicity four, Semigroup Forum 83 (2011), 468 – 478, DOI: 10.1007/s00233-011-9328-4.
J. C. Rosales and P. A. García-Sánchez, Numerical Semigroups, 1st edition, Developments in Mathematics series, Vol. 20, Springer New York, NY, ix + 181 pages, (2009), DOI: 10.1007/978-1-4419-0160-6.
J. C. Rosales, P. A. García-Sánchez, J. I. García-García and M. B. Branco, Arf numerical semigroups, Journal of Algebra 276(1) (2004), 3 – 12, DOI: 10.1016/j.jalgebra.2004.03.007.
J. J. Sylvester, Mathematical questions with their solutions, Educational Times 41 (1884), 171 – 178.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
