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Motivated by a property of linear resistive electrical networks, we introduce the class of Rayleigh matroids. These form a subclass of the balanced matroids defined by Feder and Mihail [10] in 1992. We prove a variety of results relating Rayleigh ma-troids to other well–known classes – in particular, we show that a binary matroid is Rayleigh if and only if(More)
Rayleigh monotonicity in Physics has a combinatorial interpretation. In this paper we give a combinatorial proof of the Rayleigh formula using Jacobi Identity and All Minors Matrix-Tree Theorem. Motivated by the fact that the edge set of each spanning tree of G is a basis of the graphic matroid induced by G, we define Rayleigh monotonicity of the generating(More)
The Rayleigh monotonicity is a principle from the theory of electrical networks. Its combinatorial interpretation says for each two edges of a graph G, that the presence of one of them in a random spanning tree of G is negatively correlated with the presence of the other edge. In this paper we give a self-contained (inductive) proof of Rayleigh monotonicity(More)
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