Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 51 Sayı: 1, 218 - 227, 14.02.2022
https://doi.org/10.15672/hujms.897234

Öz

Kaynakça

  • [1] 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 Amer. Math. Soc. 598, 1997.
  • [2] M.B. Branco, M.C. Faria and J.C. Rosales, Positioned numerical semigroups, Quaest. Math. 44, 679-691, 2021.
  • [3] M.B. Branco, M.C. Faria and J.C. Rosales, Almost-positioned numerical semigroups, Results Math. 76, 1-14, 2021.
  • [4] M.B. Branco, I. Ojeda and J.C. Rosales, The set of numerical semigroups of a given multiplicity and Frobenius number, Port. Math. 78, 147-167, 2021.
  • [5] R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum 35, 63-83, 1987.
  • [6] E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc. 25, 748-751, 1973.
  • [7] J.C. Rosales, On symmetric numerical semigroups, J. Algebra 182, 422-434, 1996.
  • [8] J.C. Rosales, Adding or removing on element from a Pseudo- symmetric numerical semigroup, Boll. Unione Mat. Ital. 9, 681-696, 2006.
  • [9] J.C. Rosales, Numerical semigroups that differ from a Symmetric numerical semigroups in one element, Algebra Colloq. 15, 23-32, 2008.
  • [10] J.C. Rosales and M.B. Branco, Irreducible numerical semigroups, Pacific J. Math. 209, 131-143, 2003.
  • [11] J.C. Rosales and P.A. García-Sánchez, Numerical semigroups, Springer Science & Business Media, 2009.

Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number

Yıl 2022, Cilt: 51 Sayı: 1, 218 - 227, 14.02.2022
https://doi.org/10.15672/hujms.897234

Öz

A $C$-semigroup (respectively a $D$-semigroup) is a positioned numerical semigroup $S$ such that $\rm{g}(S)=\frac{\rm{F}(S)+\rm{m}(S)-1}{2}$ (respectively $\rm{g}(S)=\frac{\rm{F}(S)+\rm{m}(S)-2}{2}$). In this paper we study these semigroups giving formulas for the Frobenius number, pseudo-Frobenius number, and type. Furthermore, we give algorithms for computing the whole set of $C$-semigroups and $D$-semigroups.

Kaynakça

  • [1] 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 Amer. Math. Soc. 598, 1997.
  • [2] M.B. Branco, M.C. Faria and J.C. Rosales, Positioned numerical semigroups, Quaest. Math. 44, 679-691, 2021.
  • [3] M.B. Branco, M.C. Faria and J.C. Rosales, Almost-positioned numerical semigroups, Results Math. 76, 1-14, 2021.
  • [4] M.B. Branco, I. Ojeda and J.C. Rosales, The set of numerical semigroups of a given multiplicity and Frobenius number, Port. Math. 78, 147-167, 2021.
  • [5] R. Fröberg, C. Gottlieb and R. Häggkvist, On numerical semigroups, Semigroup Forum 35, 63-83, 1987.
  • [6] E. Kunz, The value-semigroup of a one-dimensional Gorenstein ring, Proc. Amer. Math. Soc. 25, 748-751, 1973.
  • [7] J.C. Rosales, On symmetric numerical semigroups, J. Algebra 182, 422-434, 1996.
  • [8] J.C. Rosales, Adding or removing on element from a Pseudo- symmetric numerical semigroup, Boll. Unione Mat. Ital. 9, 681-696, 2006.
  • [9] J.C. Rosales, Numerical semigroups that differ from a Symmetric numerical semigroups in one element, Algebra Colloq. 15, 23-32, 2008.
  • [10] J.C. Rosales and M.B. Branco, Irreducible numerical semigroups, Pacific J. Math. 209, 131-143, 2003.
  • [11] J.C. Rosales and P.A. García-Sánchez, Numerical semigroups, Springer Science & Business Media, 2009.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

José Carlos Rosales 0000-0003-3353-4335

Manuel B. Branco 0000-0003-0397-7602

M. C. Faria Bu kişi benim 0000-0002-1974-7396

Yayımlanma Tarihi 14 Şubat 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 1

Kaynak Göster

APA Rosales, J. C., Branco, M. B., & Faria, M. C. (2022). Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number. Hacettepe Journal of Mathematics and Statistics, 51(1), 218-227. https://doi.org/10.15672/hujms.897234
AMA Rosales JC, Branco MB, Faria MC. Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number. Hacettepe Journal of Mathematics and Statistics. Şubat 2022;51(1):218-227. doi:10.15672/hujms.897234
Chicago Rosales, José Carlos, Manuel B. Branco, ve M. C. Faria. “Positioned Numerical Semigroups With Maximal Gender As Function of Multiplicity and Frobenius Number”. Hacettepe Journal of Mathematics and Statistics 51, sy. 1 (Şubat 2022): 218-27. https://doi.org/10.15672/hujms.897234.
EndNote Rosales JC, Branco MB, Faria MC (01 Şubat 2022) Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number. Hacettepe Journal of Mathematics and Statistics 51 1 218–227.
IEEE J. C. Rosales, M. B. Branco, ve M. C. Faria, “Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 1, ss. 218–227, 2022, doi: 10.15672/hujms.897234.
ISNAD Rosales, José Carlos vd. “Positioned Numerical Semigroups With Maximal Gender As Function of Multiplicity and Frobenius Number”. Hacettepe Journal of Mathematics and Statistics 51/1 (Şubat 2022), 218-227. https://doi.org/10.15672/hujms.897234.
JAMA Rosales JC, Branco MB, Faria MC. Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number. Hacettepe Journal of Mathematics and Statistics. 2022;51:218–227.
MLA Rosales, José Carlos vd. “Positioned Numerical Semigroups With Maximal Gender As Function of Multiplicity and Frobenius Number”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 1, 2022, ss. 218-27, doi:10.15672/hujms.897234.
Vancouver Rosales JC, Branco MB, Faria MC. Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):218-27.