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

页码：2310 / 2319

页数：10

共 50 条

[41] Distribution of genus among numerical semigroups with fixed Frobenius number
Singhal, Deepesh
SEMIGROUP FORUM, 2022, 104 (03) : 704 - 723
[42] On the enumeration of the set of saturated numerical semigroups with fixed Frobenius number
Rosales, J. C.
Branco, M. B.
Torrao, D.
APPLIED MATHEMATICS AND COMPUTATION, 2014, 236 : 471 - 479
[43] A combinatorial problem and numerical semigroups
Robles Perez, Aureliano M.
Carlos Rosales, Jose
ARS MATHEMATICA CONTEMPORANEA, 2018, 15 (02) : 323 - 336
[44] THE FROBENIUS PROBLEM FOR NUMERICAL SEMIGROUPS GENERATED BY THE THABIT NUMBERS OF THE FIRST, SECOND KIND BASE b AND THE CUNNINGHAM NUMBERS
Song, Kyunghwan
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2020, 57 (03) : 623 - 647
[45] Frobenius R-Variety of the Numerical Semigroups Contained in a Given One
J. C. Rosales
M. B. Branco
M. A. Traesel
Mediterranean Journal of Mathematics, 2022, 19
[46] Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes
Lepilov, Mikhail
O'Rourke, Joshua
Swanson, Irena
SEMIGROUP FORUM, 2015, 91 (01) : 238 - 259
[47] Frobenius R-Variety of the Numerical Semigroups Contained in a Given One
Rosales, J. C.
Branco, M. B.
Traesel, M. A.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (03)
[48] Positioned numerical semigroups with maximal gender as function of multiplicity and Frobenius number
Rosales, J. C.
Branco, M. B.
Faria, M. C.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 51 (01): : 218 - 227
[49] Frobenius numbers of numerical semigroups generated by three consecutive squares or cubes
Mikhail Lepilov
Joshua O’Rourke
Irena Swanson
Semigroup Forum, 2015, 91 : 238 - 259
[50] 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

← 1 2 3 4 5 →