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arXiv · 1310.4159

Positively oriented matroids are realizable

Federico Ardila·Felipe Rincón·Lauren Williams
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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.

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Federico Ardila, Felipe Rincón, Lauren Williams. 2013-11-02. Positively oriented matroids are realizable. https://arxiv.org/abs/1310.4159

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