English

Electrical networks and hyperplane arrangements

Combinatorics 2020-09-22 v2

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.

Keywords

Cite

@article{arxiv.1709.01227,
  title  = {Electrical networks and hyperplane arrangements},
  author = {Bob Lutz},
  journal= {arXiv preprint arXiv:1709.01227},
  year   = {2020}
}

Comments

19 pages, 4 figures

R2 v1 2026-06-22T21:33:06.367Z