On certain hyperplane arrangements and colored graphs
Joungmin Song

TL;DR
This paper establishes a bijective relationship between 3-colored graphs and specific hyperplane arrangements, enabling the computation of their characteristic polynomials through graph centrality properties.
Contribution
It introduces a novel correspondence linking 3-colored graphs with hyperplane arrangements and expresses characteristic polynomials in terms of graph centrality.
Findings
Characteristic polynomial computed for n=2,3
Centrality of graphs corresponds to hyperplane arrangement properties
New combinatorial method for analyzing hyperplane arrangements
Abstract
We exhibit a one-to-one correspondence between -colored graphs and subarrangements of certain hyperplane arrangements denoted , . We define the notion of centrality of -colored graphs which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial of can be expressed in terms of the number of central -colored graphs, and we compute for .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Finite Group Theory Research
