偏置图的罗得半网格

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

Michael J. Gottstein, Thomas Zaslavsky

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引用次数: 0

摘要

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。

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The Rhodes semilattice of a biased graph

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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