License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2020.24
URN: urn:nbn:de:0030-drops-117097
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11709/
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Loho, Georg ; Végh, László A.

Signed Tropical Convexity

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LIPIcs-ITCS-2020-24.pdf (0.7 MB)

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.

BibTeX - Entry

@InProceedings{loho_et_al:LIPIcs:2020:11709,
  author =	{Georg Loho and L{\'a}szl{\'o} A. V{\'e}gh},
  title =	{{Signed Tropical Convexity}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{24:1--24:35},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Thomas Vidick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11709},
  URN =		{urn:nbn:de:0030-drops-117097},
  doi =		{10.4230/LIPIcs.ITCS.2020.24},
  annote =	{Keywords: tropical convexity, signed tropical numbers, Farkas' lemma}
}

Keywords: tropical convexity, signed tropical numbers, Farkas' lemma
Collection: 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)
Issue Date: 2020
Date of publication: 06.01.2020

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