Dissimilarity Vectors of Trees and Their Tropical Linear Spaces (Extended Abstract)

Abstract

We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissimilarity vector and its associated family of matroids. This gives a family of complete flags of tropical linear spaces, where each flag is described by a weighted tree.

Keywords

• dissimilarity vector
• tropical linear space
• tight span
• weighted tree
• matroid polytope
• t-theory
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]