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
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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