Article ID Journal Published Year Pages File Type
4655226 Journal of Combinatorial Theory, Series A 2015 19 Pages PDF
Abstract

Let T   be a tree with a vertex set {1,2,…,N}{1,2,…,N}. Denote by dijdij the distance between vertices i and j  . In this paper, we present an explicit combinatorial formula of principal minors of the matrix (tdij)(tdij), and its applications to tropical geometry, study of multivariate stable polynomials, and representation of valuated matroids. We also give an analogous formula for a skew-symmetric matrix associated with T.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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