The Rhodes semilattice of a biased graph

IF 0.9 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2024-05-15 DOI:10.1007/s00010-024-01039-3

Michael J. Gottstein, Thomas Zaslavsky

引用次数: 0

Abstract

We reinterpret the Rhodes semilattices \(R_n({\mathfrak {G}})\) of a group \({\mathfrak {G}}\) in terms of gain graphs and generalize them to all gain graphs, both as sets of partition-potential pairs and as sets of subgraphs, and for the latter, further to biased graphs. Based on this we propose four different natural lattices in which the Rhodes semilattices and its generalizations are order ideals.

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偏置图的罗得半网格

我们从增益图的角度重新解释了组\({\mathfrak {G}})的罗兹半格（R_n({\mathfrak {G}})），并将其推广到所有增益图，既包括分区-势对的集合，也包括子图的集合，对于后者，还进一步推广到偏置图。在此基础上，我们提出了四种不同的自然网格，其中罗兹半网格及其广义是阶理想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.