English

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

R2 v1 2026-06-22T01:47:40.942Z