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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| Published in | Journal of combinatorial theory. Series A Vol. 135; pp. 291 - 331 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.10.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0097-3165 1096-0899 |
| DOI | 10.1016/j.jcta.2015.06.001 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Rincón, Felipe Fink, Alex |
| Author_xml | – sequence: 1 givenname: Alex orcidid: 0000-0003-1562-4695 surname: Fink fullname: Fink, Alex email: a.fink@qmul.ac.uk organization: School of Mathematical Sciences, Queen Mary University of London, United Kingdom – sequence: 2 givenname: Felipe surname: Rincón fullname: Rincón, Felipe email: e.f.rincon@warwick.ac.uk organization: Mathematics Institute, University of Warwick, United Kingdom |
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| Cites_doi | 10.1515/advg.2004.023 10.1016/0001-8708(92)90028-J 10.1093/qmath/22.3.435 10.1515/forum-2012-0030 10.4171/dm/154 10.17323/1609-4514-2007-7-2-327-346 10.1016/j.jctb.2005.06.004 10.1006/aima.1993.1013 10.1016/0001-8708(87)90059-4 10.1137/080716219 10.1006/aama.2000.0716 10.1007/s00209-008-0400-z 10.1093/imrn/rnn153 10.1016/j.jcta.2011.08.001 10.1112/jlms/s2-5.2.289 |
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| Keywords | Transversal matroids Stiefel map Tropical linear spaces Mixed subdivisions Matchings Matroid polytope subdivisions Tropical hyperplane arrangements |
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| SubjectTerms | Matchings Matroid polytope subdivisions Mixed subdivisions Stiefel map Transversal matroids Tropical hyperplane arrangements Tropical linear spaces |
| Title | Stiefel tropical linear spaces |
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