Weighted digraphs and tropical cones
Weighted digraphs and tropical cones
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DOI：
10.1016/j.laa.2016.02.027
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发表时间：
2016-07-15
影响因子：
1.1
通讯作者：
Loho, Georg
中科院分区：
文献类型：
--
作者：
Joswig, Michael;Loho, Georg
本文研究热带射影空间中有限点构形的组合学，或对偶地，研究多个热带超平面的排列。此外，可以通过对R-d的多面体分解进行粗化来考虑许多热带半空间的排列。这导致热带投影空间TIPmind-1的自然细胞分解。我们的方法是利用一类已知的普通凸多面体自然与加权有向图。通过这种方式，我们可以联系并使用组合数学和优化的结果。一个结果是解决了一个猜想的Reinin和Yu（2007）。(C)2016 Elsevier Inc. All rights reserved.
This paper is about the combinatorics of finite point configurations in the tropical projective space or, dually, of arrangements of finitely many tropical hyperplanes. Moreover, arrangements of finitely many tropical halfspaces can be considered via coarsenings of the resulting polyhedral decompositions of R-d. This leads to natural cell decompositions of the tropical projective space TIPmind-1. Our method is to employ a known class of ordinary convex polyhedra naturally associated with weighted digraphs. This way we can relate to and use results from combinatorics and optimization. One outcome is the solution of a conjecture of Develin and Yu (2007). (C) 2016 Elsevier Inc. All rights reserved.