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Stiefel tropical linear spaces. (English) Zbl 1321.15044
Summary: The tropical Stiefel map associates to a tropical matrix $$A$$ its tropical Plücker vector of maximal minors, and thus a tropical linear space $$L(A)$$. We call the $$L(A)$$s obtained in this way Stiefel tropical linear spaces. We prove that they are dual to certain matroid subdivisions of polytopes of transversal matroids, and we relate their combinatorics to a canonically associated tropical hyperplane arrangement. We also explore a broad connection with the secondary fan of the Newton polytope of the product of all maximal minors of a matrix. In addition, we investigate the natural parametrization of $$L(A)$$ arising from the tropical linear map defined by $$A$$.

##### MSC:
 15A80 Max-plus and related algebras 14T05 Tropical geometry (MSC2010) 52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
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