Weighted digraphs and tropical cones

Joswig, Michael and Loho, Georg (2016) Weighted digraphs and tropical cones. Linear Algebra and Its Applications, 501. pp. 304-343. ISSN 0024-3795

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Abstract

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 Rd. This leads to natural cell decompositions of the tropical projective space TPmind−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).

Item Type:	Article
Additional Information:	© 2016 Elsevier Inc.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	19 Jun 2019 12:21
Last Modified:	06 Apr 2024 17:54
URI:	http://eprints.lse.ac.uk/id/eprint/101047

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