JournalsjemsVol. 19, No. 3pp. 815–833

Positively oriented matroids are realizable

  • Federico Ardila

    San Francisco State University, USA

  • Felipe Rincón

    University of Warwick, Coventry, UK

  • Lauren K. Williams

    University of California, Berkeley, USA
Positively oriented matroids are realizable cover
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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