The Frobenius problem for numerical semigroups

被引：9
|
作者：
Rosales, J. C. [2 ]
Branco, M. B. [1 ]
机构：
[1] Univ Evora, Dept Matemat, P-7000 Evora, Portugal
[2] Univ Granada, Dept Algebra, E-18071 Granada, Spain
来源：
JOURNAL OF NUMBER THEORY | 2011年 / 131卷 / 12期
关键词：
Numerical semigroup; Frobenius number; Genus;
D O I：
10.1016/j.jnt.2011.05.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we characterize those numerical semigroups containing < n(1), n(2)>. From this characterization, we give formulas for the genus and the Frobenius number of a numerical semigroup. These results can be used to give a method for computing the genus and the Frobenius number of a numerical semigroup with embedding dimension three in terms of its minimal system of generators. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：2310 / 2319
页数：10
相关论文
共 50 条
  • [1] ON THE FROBENIUS PROBLEM OF NUMERICAL SEMIGROUPS
    Leher, Eli
    COMMUNICATIONS IN ALGEBRA, 2009, 37 (02) : 639 - 649
  • [2] The Frobenius problem for repunit numerical semigroups
    J. C. Rosales
    M. B. Branco
    D. Torrão
    The Ramanujan Journal, 2016, 40 : 323 - 334
  • [3] The Frobenius problem for Mersenne numerical semigroups
    J. C. Rosales
    M. B. Branco
    D. Torrão
    Mathematische Zeitschrift, 2017, 286 : 741 - 749
  • [4] The Frobenius problem for Thabit numerical semigroups
    Rosales, J. C.
    Branco, M. B.
    Torrao, D.
    JOURNAL OF NUMBER THEORY, 2015, 155 : 85 - 99
  • [5] The Frobenius problem for Mersenne numerical semigroups
    Rosales, J. C.
    Branco, M. B.
    Torrao, D.
    MATHEMATISCHE ZEITSCHRIFT, 2017, 286 (1-2) : 741 - 749
  • [6] The Frobenius problem for repunit numerical semigroups
    Rosales, J. C.
    Branco, M. B.
    Torrao, D.
    RAMANUJAN JOURNAL, 2016, 40 (02): : 323 - 334
  • [7] The Frobenius problem for a class of numerical semigroups
    Gu, Ze
    Tang, Xilin
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2017, 13 (05) : 1335 - 1347
  • [8] The Frobenius problem for numerical semigroups with multiplicity four
    J. C. Rosales
    M. B. Branco
    Semigroup Forum, 2011, 83 : 468 - 478
  • [9] The Frobenius problem for numerical semigroups with multiplicity four
    Rosales, J. C.
    Branco, M. B.
    SEMIGROUP FORUM, 2011, 83 (03) : 468 - 478
  • [10] The Frobenius Problem for Generalized Repunit Numerical Semigroups
    Branco, Manuel B.
    Colaco, Isabel
    Ojeda, Ignacio
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (01)
12345