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Signed tropical convexity

Loho, Georg and Végh, László A. (2020) Signed tropical convexity. In: Vidick, Thomas, (ed.) 11th Innovations in Theoretical Computer Science Conference, ITCS 2020. Leibniz International Proceedings in Informatics, LIPIcs. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, USA. ISBN 9783959771344

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Identification Number: 10.4230/LIPIcs.ITCS.2020.24

Abstract

We establish a new notion of tropical convexity for signed tropical numbers. We provide several equivalent descriptions involving balance relations and intersections of open halfspaces as well as the image of a union of polytopes over Puiseux series and hyperoperations. Along the way, we deduce a new Farkas’ lemma and Fourier-Motzkin elimination without the non-negativity restriction on the variables. This leads to a Minkowski-Weyl theorem for polytopes over the signed tropical numbers.

Item Type: Book Section
Official URL: https://drops.dagstuhl.de/opus/institut_lipics.php
Additional Information: © 2020 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 13 Feb 2020 15:03
Last Modified: 06 Aug 2020 11:06
URI: http://eprints.lse.ac.uk/id/eprint/103363

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