The Frobenius problem for numerical semigroups

被引：10
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
[21]   The set of Arf numerical semigroups with given Frobenius number [J].
Moreno-frias, Maria Angeles ;
Rosales, Jose Carlos .
TURKISH JOURNAL OF MATHEMATICS, 2023, 47 (05) :1392-1405
[22]   The tree of irreducible numerical semigroups with fixed Frobenius number [J].
Blanco, Victor ;
Carlos Rosales, Jose .
FORUM MATHEMATICUM, 2013, 25 (06) :1249-1261
[23]   THE COVARIETY OF PERFECT NUMERICAL SEMIGROUPS WITH FIXED FROBENIUS NUMBER [J].
Moreno-Frias, Maria angeles ;
Rosales, Jose Carlos .
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2024, 74 (03) :697-714
[24]   The Frobenius problem for numerical semigroups generated by sequences of the form can-d [J].
Arias, Fabian ;
Borja, Jerson ;
Rhenals, Calixto .
SEMIGROUP FORUM, 2023, 107 (03) :581-608
[25]   The genus, Frobenius number and pseudo-Frobenius numbers of numerical semigroups of type 2 [J].
Robles-Perez, Aureliano M. ;
Carlos Rosales, Jose .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (05) :1081-1090
[26]   The Frobenius number in the set of numerical semigroups with fixed multiplicity and genus [J].
Robles-Perez, Aureliano M. ;
Carlos Rosales, Jose .
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2017, 13 (04) :1003-1011
[27]   Almost symmetric numerical semigroups with given Frobenius number and type [J].
Branco, M. B. ;
Ojeda, I ;
Rosales, J. C. .
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2019, 18 (11)
[28]   On the enumeration of the set of saturated numerical semigroups with fixed Frobenius number [J].
Rosales, J. C. ;
Branco, M. B. ;
Torrao, D. .
APPLIED MATHEMATICS AND COMPUTATION, 2014, 236 :471-479
[29]   Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes [J].
Mikhail Lepilov ;
Joshua O’Rourke ;
Irena Swanson .
Semigroup Forum, 2015, 91 :238-259
[30]   Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes [J].
Lepilov, Mikhail ;
O'Rourke, Joshua ;
Swanson, Irena .
SEMIGROUP FORUM, 2015, 91 (01) :238-259
12345