Electrical networks and hyperplane arrangements

Abstract

This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic arrangements to Dirichlet arrangements, including characteristic polynomials and supersolvability. We apply these results to visibility sets of order polytopes and fixed-energy harmonic functions on electrical networks.

19 pages, 4 figures

References in corpus (3)

• The maximum likelihood degree of a very affine variety
• On the monodromy action on Milnor fibers of graphic arrangements
• Vertex-weighted graphs and freeness of $\psi$-graphical arrangements

Cited by in corpus (1)

• Matroids arising from electrical networks