Rank three matroids are Rayleigh

TL;DR

This paper proves that all matroids of rank three satisfy Rayleigh inequalities, extending the Rayleigh property from electrical networks to a broader class of matroids.

Contribution

It establishes that every rank three matroid inherently satisfies Rayleigh inequalities, a property previously studied mainly in electrical network contexts.

Findings

All rank three matroids satisfy Rayleigh inequalities.

Rayleigh property extends beyond electrical networks to matroids.

Provides a new class of matroids with Rayleigh property.

Abstract

A Rayleigh matroid is one which satisfies a set of inequalities analogous to the Rayleigh monotonicity property of linear resistive electrical networks. We show that every matroid of rank three satisfies these inequalities.