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ON CERTAIN HYPERPLANE ARRANGEMENTS AND COLORED GRAPHS

  • Received : 2015.03.05
  • Published : 2017.03.31

Abstract

We exhibit a one-to-one correspondence between 3-colored graphs and subarrangements of certain hyperplane arrangements denoted ${\mathcal{J}}_n$, $n{\in}{\mathbb{N}}$. We define the notion of centrality of 3-colored graphs, which corresponds to the centrality of hyperplane arrangements. Via the correspondence, the characteristic polynomial ${\chi}{\mathcal{J}}_n$ of ${\mathcal{J}}_n$ can be expressed in terms of the number of central 3-colored graphs, and we compute ${\chi}{\mathcal{J}}_n$ for n = 2, 3.

Acknowledgement

Supported by : GIST Research Institute

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  1. Enumerating Hassett’s Wall and Chamber Decomposition of the Moduli Space of Weighted Stable Curves pp.1944-950X, 2018, https://doi.org/10.1080/10586458.2018.1428132