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 49 条
  • [31] The set of numerical semigroups of a given genus
    Blanco, V.
    Rosales, J. C.
    SEMIGROUP FORUM, 2012, 85 (02) : 255 - 267
  • [32] Frobenius pseudo-variety of numerical semigroups with a given multiplicity and ratio
    Moreno-Frias, M. A.
    Rosales, J. C.
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2023, 36 (3) : 427 - 441
  • [33] On the Classification of Telescopic Numerical Semigroups of Some Fixed Multiplicity
    Wang, Ying
    Binyamin, Muhammad Ahsan
    Amin, Iqra
    Aslam, Adnan
    Rao, Yongsheng
    MATHEMATICS, 2022, 10 (20)
  • [34] Numerical semigroups with a given set of pseudo-Frobenius numbers
    Delgado, M.
    Garcia-Sanchez, P. A.
    Robles-Perez, A. M.
    LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2016, 19 (01): : 186 - 205
  • [35] The Frobenius number of a family of numerical semigroups with embedding dimension 5
    Herzinger, Kurt
    McLaughlin, Emelia
    Trimber, Julie
    INVOLVE, A JOURNAL OF MATHEMATICS, 2023, 16 (05): : 833 - 847
  • [36] Almost symmetric numerical semigroups with given Frobenius number and type
    Branco, M. B.
    Ojeda, I
    Rosales, J. C.
    JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2019, 18 (11)
  • [37] On certain families of sparse numerical semigroups with Frobenius number even
    Tizziotti, Guilherme
    Villanueva, Juan
    ALGEBRA AND DISCRETE MATHEMATICS, 2019, 27 (01): : 99 - 116
  • [38] Bounds on the number of numerical semigroups of a given genus
    Bras-Amoros, Maria
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2009, 213 (06) : 997 - 1001
  • [39] The Number of Saturated Numerical Semigroups with a Determinate Genus
    Rosales, J. C.
    Branco, M. B.
    Torrao, D.
    DYNAMICS, GAMES AND SCIENCE, 2015, 1 : 607 - 616
  • [40] Families of numerical semigroups closed under finite intersections and for the Frobenius number
    Rosales, J. C.
    HOUSTON JOURNAL OF MATHEMATICS, 2008, 34 (02): : 339 - 348
12345