Stiefel tropical linear spaces
Stiefel tropical linear spaces
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DOI：
10.1016/j.jcta.2015.06.001
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发表时间：
2015-10-01
影响因子：
1.1
通讯作者：
Rincon, Felipe
中科院分区：
文献类型：
--
作者：
Fink, Alex;Rincon, Felipe
热带Stiefel映射将热带矩阵A与其热带Plucker向量的极大子式相关联，从而与热带线性空间L（A）相关联。我们称这样得到的L（A）s为Stiefel热带线性空间。我们证明了它们是对偶的某些拟阵细分多面体的横截拟阵，我们与他们的组合的一个典型的相关热带超平面安排。我们还探讨了一个广泛的连接与次风扇的牛顿多面体的产品的所有最大的未成年人的矩阵。此外，我们还研究了由A. (C)2015 Elsevier Inc. All rights reserved.
The tropical Stiefel map associates to a tropical matrix A its tropical Plucker 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. (C) 2015 Elsevier Inc. All rights reserved.