Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ENUMERATION OF GRAPHS AND THE CHARACTERISTIC POLYNOMIAL OF THE HYPERPLANE ARRANGEMENTS 𝒥n

  • Song, Joungmin (Division of Liberal Arts & Sciences Gwangju Institute of Science and Technology)
  • Received : 2016.09.04
  • Accepted : 2017.03.03
  • Published : 2017.09.01
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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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References

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