Geodesic
Positively oriented matroids are realizable
Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 815-833.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/680
Classification : 05-XX, 14-XX, 52-XX
Keywords: Oriented matroid, positroid, matroid polytope, total positivity, Grassmannian, Mac-Phersonian 
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Federico Ardila; Felipe Rincón; Lauren K. Williams. Positively oriented matroids are realizable. Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 815-833. doi : 10.4171/jems/680. http://geodesic.mathdoc.fr/articles/10.4171/jems/680/

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