Geodesic
Positively oriented matroids are realizable
Journal of the European Mathematical Society, Tome 19 (2017) no. 3, pp. 815-833 Cet article a éte moissonné depuis la source EMS Press

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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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     author = {Federico Ardila and Felipe Rinc\'on and Lauren K. Williams},
     title = {Positively oriented matroids are realizable},
     journal = {Journal of the European Mathematical Society},
     pages = {815--833},
     year = {2017},
     volume = {19},
     number = {3},
     doi = {10.4171/jems/680},
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}
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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

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