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

页码：433 / 442

页数：10

共 49 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 enumeration of the set of atomic numerical semigroups with fixed Frobenius number
Robles-Perez, Aureliano M.
Carlos Rosales, Jose
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (08)
[4] 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
[5] On the Enumeration of the Set of Numerical Semigroups with Fixed Frobenius Number and Fixed Number of Second Kind Gaps
Aureliano M. Robles-Pérez
José Carlos Rosales
Results in Mathematics, 2022, 77
[6] On the Enumeration of the Set of Numerical Semigroups with Fixed Frobenius Number and Fixed Number of Second Kind Gaps
Robles-Perez, Aureliano M.
Carlos Rosales, Jose
RESULTS IN MATHEMATICS, 2022, 77 (01)
[7] 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
[8] Atoms of the set of numerical semigroups with fixed Frobenius number
Rosales, J. C.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (01) : 41 - 51
[9] Distribution of genus among numerical semigroups with fixed Frobenius number
Deepesh Singhal
Semigroup Forum, 2022, 104 : 704 - 723
[10] Distribution of genus among numerical semigroups with fixed Frobenius number
Singhal, Deepesh
SEMIGROUP FORUM, 2022, 104 (03) : 704 - 723

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