Signed tropical convexity
Optimization and Control
2019-10-03 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.1906.06686,
title = {Signed tropical convexity},
author = {Georg Loho and László A. Végh},
journal= {arXiv preprint arXiv:1906.06686},
year = {2019}
}
Comments
v1: 30 pages, 7 figures; v2: 31 pages, 7 figures, small improvements and major restructuring