Circular Planar Electrical Networks I : The Electrical Poset EP n

@inproceedings{Alman2013CircularPE,
  title={Circular Planar Electrical Networks I : The Electrical Poset EP n},
  author={Joshua Alman and Carl Lian and Brandon Tran},
  year={2013}
}
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 EPn of electrical networks with n boundary vertices, giving two equivalent characterizations, one combinatorial and the other topological. We then investigate various properties of the EPn, proving that it is graded by number of edges of critical representatives. Finally, we answer various enumerative questions related to EPn, adapting… CONTINUE READING