Signed tropical convexity

(2020) Signed tropical convexity In: 11th Innovations in Theoretical Computer Science Conference, ITCS 2020. Leibniz International Proceedings in Informatics, LIPIcs . Schloss Dagstuhl, Leibniz-Zentrum für Informatik. ISBN 9783959771344

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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	Chapter
Keywords	Farkas’ lemma,Signed tropical numbers,Tropical convexity
Departments	Mathematics
DOI	10.4230/LIPIcs.ITCS.2020.24
Date Deposited	13 Feb 2020 15:03
URI	https://researchonline.lse.ac.uk/id/eprint/103363

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http://www.scopus.com/inward/record.url?scp=85078018402&partnerID=8YFLogxK (Scopus publication)
http://www.lse.ac.uk/Mathematics/people/Laszlo-Vegh (Author)
http://www.lse.ac.uk/Mathematics/people/Georg-Loho (Author)
https://drops.dagstuhl.de/opus/institut_lipics.php (Official URL)

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