Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655226 | Journal of Combinatorial Theory, Series A | 2015 | 19 Pages |
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
Authors
Hiroshi Hirai, Akihiro Yabe,