Stiefel tropical linear spaces

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 transver...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 135; pp. 291 - 331
Main Authors Fink, Alex, Rincón, Felipe
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2015
Subjects
Matchings
Matroid polytope subdivisions
Mixed subdivisions
Stiefel map
Transversal matroids
Tropical hyperplane arrangements
Tropical linear spaces
Transversal matroids
Stiefel map
Tropical linear spaces
Mixed subdivisions
Matchings
Matroid polytope subdivisions
Tropical hyperplane arrangements
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ISSN0097-3165
1096-0899
DOI10.1016/j.jcta.2015.06.001

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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.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2015.06.001