Signed tropical convexity
Loho, G. & Végh, L. A.
(2020).
Signed tropical convexity.
In
Vidick, T.
(Ed.),
11th Innovations in Theoretical Computer Science Conference, ITCS 2020
.
Schloss Dagstuhl, Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.ITCS.2020.24
(2020).
Signed tropical convexity.
In
Vidick, T.
(Ed.),
11th Innovations in Theoretical Computer Science Conference, ITCS 2020
.
Schloss Dagstuhl, Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.ITCS.2020.24
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.
