Signed tropical convexity

Georg Loho, László A. Végh

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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.

Original languageEnglish
Title of host publication11th Innovations in Theoretical Computer Science Conference, ITCS 2020
EditorsThomas Vidick
PublisherDagstuhl
ISBN (Electronic)9783959771344
DOIs
Publication statusPublished - Jan 2020
Externally publishedYes
Event11th Innovations in Theoretical Computer Science Conference, ITCS 2020 - Seattle, United States
Duration: 12 Jan 202014 Jan 2020
Conference number: 11

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume151
ISSN (Print)1868-8969

Conference

Conference11th Innovations in Theoretical Computer Science Conference, ITCS 2020
Abbreviated titleITCS 2020
Country/TerritoryUnited States
CitySeattle
Period12/01/2014/01/20

Keywords

  • Farkas’ lemma
  • Signed tropical numbers
  • Tropical convexity

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