Positively oriented matroids are realizable
Combinatorics
2013-11-05 v3
Abstract
We prove da Silva's 1987 conjecture that any positively oriented matroid is a positroid; that is, it can be realized by a set of vectors in a real vector space. It follows from this result and a result of the third author that the positive matroid Grassmannian (or positive MacPhersonian) is homeomorphic to a closed ball.
Keywords
Cite
@article{arxiv.1310.4159,
title = {Positively oriented matroids are realizable},
author = {Federico Ardila and Felipe Rincón and Lauren Williams},
journal= {arXiv preprint arXiv:1310.4159},
year = {2013}
}
Comments
20 pages, 3 figures, references added