• Corpus ID: 14390221

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

@article{Alman2013CircularPE,
title={Circular Planar Electrical Networks I: The Electrical Poset EP\_\{n\}},
author={Josh Alman and Carl Lian and Brandon Tran},
journal={arXiv: Combinatorics},
year={2013}
}
• Published 11 September 2013
• Mathematics, Computer Science
• arXiv: Combinatorics
Following de Verdi ere-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…
8 Citations

## Figures from this paper

### The Space of Circular Planar Electrical Networks

• Mathematics
SIAM J. Discret. Math.
• 2017
This work discusses several parametrizations of the space of circular planar electrical networks, and shows how to test if a network with n nodes is well-connected by checking that $\binom{n}{2}$ minors of the $n\times n$ response matrix are positive.

### Novel Relationships Between Circular Planar Graphs and Electrical Networks

• Mathematics
• 2016
Circular planar graphs are used to model electrical networks, which arise in classical physics. Associated with such a network is a network response matrix, which carries information about how the

### SIF Permutations and Chord-Connected Permutations

A stabilized-interval-free (SIF) permutation on [n], introduced by Callan, is a permutation that does not stabilize any proper interval of [n]. Such permutations are known to be the irreducibles in

### Stabilized-Interval-Free Permutations and Chord-Connected Permutations

A stabilized-interval-free (SIF) permutation on [n], introduced by Callan, is a permutation that does not stabilize any proper interval of [n]. Such permutations are known to be the irreducibles in

### A Compositional Framework for Passive Linear Networks

• Mathematics
• 2015
Passive linear networks are used in a wide variety of engineering applications, but the best studied are electrical circuits made of resistors, inductors and capacitors. We describe a category where

### Transfer of status qualifying dissertation : a compositional approach to control theory

This paper proposes a programme of research with the aim of understanding network-based systems through the application of monoidal category theory, and outlines some in-progress work in this

## References

SHOWING 1-10 OF 13 REFERENCES

### Mobius functions of lattices

• Mathematics
• 1997
Abstract We introduce the concept of a bounded below set in a lattice. This can be used to give a generalization of Rota's broken circuit theorem to any finite lattice. We then show how this result

### Counting stabilized-interval-free permutations

A stabilized-interval-free (SIF) permutation on [n]={1,2,...,n} is one that does not stabilize any proper subinterval of [n]. By presenting a decomposition of an arbitrary permutation into a list of

### The distribution of crossings of chords joining pairs of $2n$ points on a circle

This paper, in the first place, calls attention to an extraordinarily compact solution of the problem in the title, given (a trifle hidden) in the work of the late Jacques Touchard. Its main weight,

### The On-Line Encyclopedia of Integer Sequences

• N. Sloane
• Computer Science
Electron. J. Comb.
• 1994
The On-Line Encyclopedia of Integer Sequences (or OEIS) is a database of some 130000 number sequences which serves as a dictionary, to tell the user what is known about a particular sequence and is widely used.

### Reseaux électriques planaires II

• Mathematics
• 1994
Nutzungsbedingungen Mit dem Zugriff auf den vorliegenden Inhalt gelten die Nutzungsbedingungen als akzeptiert. Die angebotenen Dokumente stehen für nicht-kommerzielle Zwecke in Lehre, Forschung und