数字半群的算术变种

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-05-22 DOI:10.1007/s00025-024-02212-5

Manuel B. Branco, Ignacio Ojeda, José Carlos Rosales

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引用次数: 0

摘要

在本文中，我们提出了数字半群的算术变种概念。我们研究了与这些种类相关的各个方面，例如包含一组数字半群的最小算术，并展示了与算术种类相关的有根树。这棵树不是局部有限的；但是，如果弗罗贝尼斯数是固定的，这棵树就有有限多个节点，就可以开发出算法。本文提供的所有算法都包括在 GAP 中的实现（未调试）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Arithmetic Varieties of Numerical Semigroups

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Arithmetic Varieties of Numerical Semigroups

In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the rooted tree associated with an arithmetic variety. This tree is not locally finite; however, if the Frobenius number is fixed, the tree has finitely many nodes and algorithms can be developed. All algorithms provided in this article include their (non-debugged) implementation in GAP.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.