A combinatorial formula for principal minors of a matrix with tree-metric exponents and its applications

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:133

Article

Hirai, Hiroshi¹  Yabe, Akihiro¹ 

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Tokyo 1138656, Japan

关键词: Tree metric;    Valuated matroid;    M-convex function;    Tropical geometry;    Dissimilarity map;    Half-plane property;   

DOI  :  10.1016/j.jcta.2015.02.005

来源: Elsevier

【 摘 要 】

Let T be a tree with a vertex set {1, 2 ,..., N}. Denote by d(ij) the distance between vertices i and j. In this paper, we present an explicit combinatorial formula of principal minors of the matrix (t(dij)), 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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