Positively oriented matroids are realizable
Federico Ardila
San Francisco State University, USAFelipe Rincón
University of Warwick, Coventry, UKLauren K. Williams
University of California, Berkeley, USA
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.
Cite this article
Federico Ardila, Felipe Rincón, Lauren K. Williams, Positively oriented matroids are realizable. J. Eur. Math. Soc. 19 (2017), no. 3, pp. 815–833
DOI 10.4171/JEMS/680