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arXiv · 1309.2697

Circular Planar Electrical Networks I: The Electrical Poset EP_{n}

Joshua Alman·Carl Lian·Brandon Tran
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Abstract

Following de Verdière-Gitler-Vertigan and Curtis-Ingerman-Morrow, we prove a host of new results on circular planar electrical networks. We introduce a poset EP_{n} of electrical networks with n boundary vertices, giving two equivalent characterizations, one combinatorial and the other topological. We then investigate various properties of the EP_{n}, proving that it is graded by number of edges of critical representatives. Finally, we answer various enumerative questions related to EP_{n}, adapting methods of Callan and Stein-Everett.

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Joshua Alman, Carl Lian, Brandon Tran. 2013-09-11. Circular Planar Electrical Networks I: The Electrical Poset EP_{n}. https://arxiv.org/abs/1309.2697

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