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All Triply Telescopic Numerical Semigroups with Multiplicity 12

Year 2024, Volume: 10 Issue: 2, 623 - 631, 31.12.2024

Ahmet Çelik

https://doi.org/10.29132/ijpas.1579207

Abstract

Numerical semigroups form a subset of non-negative integers. Of these semigroups, symmetric ones have an important place. It is of particular importance to examine and classify telescopic numerical semigroups, which form a class of symmetric numerical semigroups. Especially finding their Frobenius numbers and spaces is a problem in itself. In this study, we will examine some telescopic numerical semigroups that will contribute to the solution to this problem. Here we will characterize all telescopic numerical semigroups produced by three elements with multiplicity 12. We will also give formulas to calculate the genus, determine number and Frobenius number in these semigroups.

Keywords

telescopic numerical semigroup frobenius genus

References

  • Sylvester, J. J. (1884). Mathematical questions with their solutions. Educational times, 41(21), 171-178.
  • Delgado, M., and García-Sánchez, P. A. (2016). numericalsgps, a GAP package for numerical semigroups. ACM Communications in Computer Algebra, 50(1), 12-24.
  • Feng, G. L., and Rao, T. R. (1994). A simple approach for construction of algebraic-geometric codes from affine plane curves. IEEE Transactions on Information Theory, 40(4), 1003-1012.
  • Hoholdt, T., and Pellikaan, R. (1995). On the decoding of algebraic-geometric codes. IEEE Transactions on Information Theory, 41(6), 1589-1614.
  • Bras-Amorós, M. (2013). Numerical semigroups and codes. In Algebraic geometry modeling in information theory (pp. 167-218).
  • Fröberg, R., Gottlieb, C., and Häggkvist, R. (1986, December). On numerical semigroups. In Semigroup forum (Vol. 35, pp. 63-83). Springer-Verlag.
  • Rosales, J.C., and Garcia-Sanchez, P.A. (2009). Numerical Semigroups. In Developments in Mathematics, Springer, New York, USA.
  • Curtis, F. (1990). On formulas for the Frobenius number of a numerical semigroup. Mathematica Scandinavica, 190-192.
  • Assi, A., and García-Sánchez, P. A. (2014). Numerical semigroups and applications. arXiv pre-print arXiv:1411.6093.
  • Rosales, J. C. (1996). On symmetric numerical semigroups. Journal of Algebra, 182(2), 422-434.
  • Matthews, G. L. (2002). On triply-generated telescopic semigroups and chains of semi-groups. Congressus Numerantium, 117-124.
  • Kirfel, C., and Pellikaan, R. (1995). The minimum distance of codes in an array coming from telescopic semigroups. IEEE Transactions on information theory, 41(6), 1720-1732.
  • García-Sánchez, P. A., Heredıa, B. A., and Leamer, M. J. (2016). Apery sets and Feng-Rao numbers over telescopic numerical semigroups. arXiv preprint arXiv:1603.09301.
  • Ilhan, S. (2006). On a class of telescopic numerical semigroups. Int. J. Contemporary Math. Sci, 1(2), 81-83.
  • Süer, M., and İlhan, S. (2019). All telescopic numerical semigroups with multiplicity four and six. Journal of Science and Technology, Erzincan Üniversitesi, 12(1), 457-462.
  • Süer, M., and İlhan, S. (2019). On telescopic numerical semigroup families with embedding dimension 3. Erzincan University Journal of Science and Technology, 12(1), 457-462.
  • Süer, M., and İlhan, S. (2020). On triply generated telescopic semigroups with multiplicity 8 and 9. Comptes rendus de l’Academie Bulgare des Sciences,72(3),315-319.
  • Süer, M., and İlhan, S. (2022). Telescopic numerical semigroups with multiplicity Ten and em-bedding dimension three. Journal of Universal Mathematics, 5(2), 139-148.
  • Wang, Y., Binyamin, M. A., Amin, I., Aslam, A., and Rao, Y. (2022). On the Classification of Telescopic Numerical Semigroups of Some Fixed Multiplicity. Mathematics, 10(20), 3871.

Katlılığı 12 Olan Bütün Üçlü Teleskopik Sayısal Yarıgruplar

Year 2024, Volume: 10 Issue: 2, 623 - 631, 31.12.2024

Ahmet Çelik

https://doi.org/10.29132/ijpas.1579207

Abstract

Sayısal yarıgruplar, negative olmayan tam sayıların bir alt kümesini oluştururlar. Bu sayısal yarıgruplardan simetrik olanlar önemli bir yere sahiptir. Simetrik sayısal yarıgrupların bir sınıfını oluşturan teleskopik sayısal yarıgrupları incelemek ve bun-ları sınıflandırmak ayrı bir önem taşımaktadır. Özellikle bu sayısal yarıgrupların Frobenius sayılarını ve boşluklarını bulmak başlı başına bir problemdir. Bu çalışmada bu probleme çözüm için bir katkı sağlayacak bazı teleskopik sayısal yarıgrupları inceleyeceğiz. Burada, katlılığı 12 olan, üç elemanla üretilen tüm teleskopik sayısal yarıgrupları karakterize edeceğiz. Ayrıca bu yarıgruplarda cins, belirteç sayısı ve Frobenius sayısını hesaplamak için formüller vereceğiz.

Keywords

teleskopik sayısal yarıgrup frobenius cins

References

  • Sylvester, J. J. (1884). Mathematical questions with their solutions. Educational times, 41(21), 171-178.
  • Delgado, M., and García-Sánchez, P. A. (2016). numericalsgps, a GAP package for numerical semigroups. ACM Communications in Computer Algebra, 50(1), 12-24.
  • Feng, G. L., and Rao, T. R. (1994). A simple approach for construction of algebraic-geometric codes from affine plane curves. IEEE Transactions on Information Theory, 40(4), 1003-1012.
  • Hoholdt, T., and Pellikaan, R. (1995). On the decoding of algebraic-geometric codes. IEEE Transactions on Information Theory, 41(6), 1589-1614.
  • Bras-Amorós, M. (2013). Numerical semigroups and codes. In Algebraic geometry modeling in information theory (pp. 167-218).
  • Fröberg, R., Gottlieb, C., and Häggkvist, R. (1986, December). On numerical semigroups. In Semigroup forum (Vol. 35, pp. 63-83). Springer-Verlag.
  • Rosales, J.C., and Garcia-Sanchez, P.A. (2009). Numerical Semigroups. In Developments in Mathematics, Springer, New York, USA.
  • Curtis, F. (1990). On formulas for the Frobenius number of a numerical semigroup. Mathematica Scandinavica, 190-192.
  • Assi, A., and García-Sánchez, P. A. (2014). Numerical semigroups and applications. arXiv pre-print arXiv:1411.6093.
  • Rosales, J. C. (1996). On symmetric numerical semigroups. Journal of Algebra, 182(2), 422-434.
  • Matthews, G. L. (2002). On triply-generated telescopic semigroups and chains of semi-groups. Congressus Numerantium, 117-124.
  • Kirfel, C., and Pellikaan, R. (1995). The minimum distance of codes in an array coming from telescopic semigroups. IEEE Transactions on information theory, 41(6), 1720-1732.
  • García-Sánchez, P. A., Heredıa, B. A., and Leamer, M. J. (2016). Apery sets and Feng-Rao numbers over telescopic numerical semigroups. arXiv preprint arXiv:1603.09301.
  • Ilhan, S. (2006). On a class of telescopic numerical semigroups. Int. J. Contemporary Math. Sci, 1(2), 81-83.
  • Süer, M., and İlhan, S. (2019). All telescopic numerical semigroups with multiplicity four and six. Journal of Science and Technology, Erzincan Üniversitesi, 12(1), 457-462.
  • Süer, M., and İlhan, S. (2019). On telescopic numerical semigroup families with embedding dimension 3. Erzincan University Journal of Science and Technology, 12(1), 457-462.
  • Süer, M., and İlhan, S. (2020). On triply generated telescopic semigroups with multiplicity 8 and 9. Comptes rendus de l’Academie Bulgare des Sciences,72(3),315-319.
  • Süer, M., and İlhan, S. (2022). Telescopic numerical semigroups with multiplicity Ten and em-bedding dimension three. Journal of Universal Mathematics, 5(2), 139-148.
  • Wang, Y., Binyamin, M. A., Amin, I., Aslam, A., and Rao, Y. (2022). On the Classification of Telescopic Numerical Semigroups of Some Fixed Multiplicity. Mathematics, 10(20), 3871.
There are 19 citations in total.

Details

Primary Language English
Subjects Robotics
Journal Section Articles
Authors

Ahmet Çelik 0000-0001-5980-0625

Early Pub Date December 30, 2024
Publication Date December 31, 2024
Submission Date November 4, 2024
Acceptance Date December 26, 2024
Published in Issue Year 2024 Volume: 10 Issue: 2

Cite

APA Çelik, A. (2024). All Triply Telescopic Numerical Semigroups with Multiplicity 12. International Journal of Pure and Applied Sciences, 10(2), 623-631. https://doi.org/10.29132/ijpas.1579207
AMA Çelik A. All Triply Telescopic Numerical Semigroups with Multiplicity 12. International Journal of Pure and Applied Sciences. December 2024;10(2):623-631. doi:10.29132/ijpas.1579207
Chicago Çelik, Ahmet. “All Triply Telescopic Numerical Semigroups With Multiplicity 12”. International Journal of Pure and Applied Sciences 10, no. 2 (December 2024): 623-31. https://doi.org/10.29132/ijpas.1579207.
EndNote Çelik A (December 1, 2024) All Triply Telescopic Numerical Semigroups with Multiplicity 12. International Journal of Pure and Applied Sciences 10 2 623–631.
IEEE A. Çelik, “All Triply Telescopic Numerical Semigroups with Multiplicity 12”, International Journal of Pure and Applied Sciences, vol. 10, no. 2, pp. 623–631, 2024, doi: 10.29132/ijpas.1579207.
ISNAD Çelik, Ahmet. “All Triply Telescopic Numerical Semigroups With Multiplicity 12”. International Journal of Pure and Applied Sciences 10/2 (December 2024), 623-631. https://doi.org/10.29132/ijpas.1579207.
JAMA Çelik A. All Triply Telescopic Numerical Semigroups with Multiplicity 12. International Journal of Pure and Applied Sciences. 2024;10:623–631.
MLA Çelik, Ahmet. “All Triply Telescopic Numerical Semigroups With Multiplicity 12”. International Journal of Pure and Applied Sciences, vol. 10, no. 2, 2024, pp. 623-31, doi:10.29132/ijpas.1579207.
Vancouver Çelik A. All Triply Telescopic Numerical Semigroups with Multiplicity 12. International Journal of Pure and Applied Sciences. 2024;10(2):623-31.
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