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arXiv · 1709.01227

Electrical networks and hyperplane arrangements

Bob Lutz
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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.

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Bob Lutz. 2018-05-12. Electrical networks and hyperplane arrangements. https://doi.org/10.1016/j.aam.2019.07.003

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