Arf numerical semigroups with prime multiplicity

被引：0
作者：
Halil İbrahim Karakaş
机构：
[1] Başkent University,Faculty of Commercial Science
来源：
Semigroup Forum | 2022年 / 105卷
关键词：
Numerical semigroups; Arf numerical semigroups; Multiplicity; Conductor; Frobenius number; Ratio;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the literature, parametrizations are given for Arf numerical semigroups with small multiplicity and arbitrary conductor. From those parametrizations, formulas are obtained for the number of such Arf numerical semigroups. These formulas show that the number of Arf numerical semigroups with multiplicity 3, 5 or 7 and arbitrary conductor depends only on the congruence class of the conductor modulo the multiplicity. In a recent work with S. İlhan and M. Süer, observing that the same is true for Arf numerical semigroups with multiplicity 11 and 13, we asked if that was true for Arf numerical semigroups with arbitrary prime multiplicity. In the present work this question is answered affirmatively.
引用
收藏
页码：478 / 487
页数：9
相关论文
共 15 条
  • [1] Arf C(1949)Une interprétation algébrique de la suite ordres de multiplicité d’une branche algébrique Proc. London Math. Soc. 20 256-287
  • [2] Barucci V(1997)Maximality properties in numerical semigroups and applications to one-dimensional analytically irreducible local domains Memoirs Amer. Math. Soc. 125 1-77
  • [3] Dobbs DE(2000)On the parameters of algebraic geometry codes related to Arf semigroups IEEE Trans. Inform. Theory 46 2634-2638
  • [4] Fontana M(2022)Arf numerical semigroups with multiplicity Turk. J. Math. 46 1446-1458
  • [5] Compillo A(2012) and Le Mathematiche 67 75-80
  • [6] Farran JI(2004)On the relation between Betti number of an Arf semigroup and its blowup J. Algebra 276 3-12
  • [7] Munuera C(undefined)Arf numerical semigroups undefined undefined undefined-undefined
  • [8] Karakaş Hİ(undefined)undefined undefined undefined undefined-undefined
  • [9] İlhan S(undefined)undefined undefined undefined undefined-undefined
  • [10] Süer M(undefined)undefined undefined undefined undefined-undefined
12