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

Abstract

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1\le i,j,k,l\le n$. 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.

References in corpus (2)

• On certain hyperplane arrangements and colored graphs
• Enumeration of graphs with given weighted number of connected components