Computing tropical linear spaces
نویسندگان
چکیده
منابع مشابه
Tropical Linear Spaces
We define tropical analogues of the notions of linear space and Plücker coordinate and study their combinatorics. We introduce tropical analogues of intersection and dualization and define a tropical linear space built by repeated dualization and transverse intersection to be constructible. Our main result that all constructible tropical linear spaces have the same f -vector and are “series-par...
متن کاملTropical Linear Spaces and Tropical Convexity
In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the conv...
متن کاملRepresenting Tropical Linear Spaces by Circuits
We study representations of tropical linear spaces as intersections of tropical hyperplanes of circuits. For several classes of matroids, we describe minimal tropical bases. We also show that every realizable tropical linear space has a natural, tropically linear parametrization involving its cocircuits. Résumé. Nous étudions les représentations des espaces vectoriels tropicaux comme intersecti...
متن کاملStar-convex functions on tropical linear spaces of complete graphs
Given a fan ∆ and a cone σ ∈ ∆, let star(σ) be the set of cones that contain σ and are one dimension bigger than σ. In this paper we study two cones of piecewise linear functions defined on ∆: the cone of functions which are convex on star(σ) for all cones, and the cone of functions which are convex on star(σ) for all cones of codimension 1. We give nice combinatorial descriptions for these two...
متن کاملDissimilarity Vectors of Trees and Their Tropical Linear Spaces ( Extended
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, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2013
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2012.03.008