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arXiv · 1701.07313

Enumeration of Graphs and the Characteristic Polynomial of the Hyperplane Arrangements $\mathcal{J}_n$

Joungmin Song
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Abstract

We give a complete formula for the characteristic polynomial of hyperplane arrangements $\mathcal J_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $ 1\leq i, j, k, l\leq n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

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Joungmin Song. 2017-01-25. Enumeration of Graphs and the Characteristic Polynomial of the Hyperplane Arrangements $\mathcal{J}_n$. https://arxiv.org/abs/1701.07313

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