ON THE ENUMERATION OF THE SET OF ELEMENTARY NUMERICAL SEMIGROUPS WITH FIXED MULTIPLICITY, FROBENIUS NUMBER OR GENUS

被引：3
|
作者：
ROSALES, J. C. [1 ]
BRANCO, M. B. [2 ]
机构：
[1] Univ Granada, Dept Algebra, E-18071 Granada, Spain
[2] Univ Evora, Dept Matemat, P-7000 Evora, Portugal
来源：
KRAGUJEVAC JOURNAL OF MATHEMATICS | 2022年 / 46卷 / 03期
关键词：
Elementary numerical semigroups; Fibonacci sequence; genus; Frobenius number and multiplicity;
D O I：
10.46793/KgJMat2203.433R
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give algorithms that allow to compute the set of every elementary numerical semigroups with given genus, Frobenius number and multiplicity. As a consequence we obtain formulas for the cardinality of these sets.
引用
收藏
页码：433 / 442
页数：10
相关论文
共 21 条
  • [1] The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus
    Robles-Perez, Aureliano M.
    Carlos Rosales, Jose
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2017, 13 (04) : 1003 - 1011
  • [2] On the enumeration of the set of numerical semigroups with fixed Frobenius number
    Blanco, V.
    Rosales, J. C.
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2012, 63 (07) : 1204 - 1211
  • [3] The set of numerical semigroups of a given multiplicity and Frobenius number
    Branco, Manuel B.
    Ojeda, Ignacio
    Carlos Rosales, Jose
    PORTUGALIAE MATHEMATICA, 2021, 78 (02) : 147 - 167
  • [4] Distribution of genus among numerical semigroups with fixed Frobenius number
    Singhal, Deepesh
    SEMIGROUP FORUM, 2022, 104 (03) : 704 - 723
  • [5] Distribution of genus among numerical semigroups with fixed Frobenius number
    Deepesh Singhal
    Semigroup Forum, 2022, 104 : 704 - 723
  • [6] The covariety of numerical semigroups with fixed Frobenius number
    Moreno-Frias, M. A.
    Rosales, J. C.
    JOURNAL OF ALGEBRAIC COMBINATORICS, 2024, 60 (02) : 555 - 568
  • [7] THE COVARIETY OF PERFECT NUMERICAL SEMIGROUPS WITH FIXED FROBENIUS NUMBER
    Moreno-Frias, Maria angeles
    Rosales, Jose Carlos
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2024, 74 (03) : 697 - 714
  • [8] On the Frobenius number and genus of a collection of semigroups generalizing repunit numerical semigroups
    Liu, Feihu
    Xin, Guoce
    Ye, Suting
    Yin, Jingjing
    SEMIGROUP FORUM, 2025, : 357 - 383
  • [9] On the enumeration of the set of saturated numerical semigroups of a given genus
    Rosales, J. C.
    Branco, M. B.
    Torrao, D.
    SEMIGROUP FORUM, 2014, 88 (03) : 621 - 630
  • [10] On the enumeration of the set of saturated numerical semigroups of a given genus
    J. C. Rosales
    M. B. Branco
    D. Torrão
    Semigroup Forum, 2014, 88 : 621 - 630
123