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arXiv · 1303.7451

Tropical convexity over max-min semiring

Viorel Nitica·Sergei Sergeev
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Abstract

This is a survey on an analogue of tropical convexity developed over the max-min semiring, starting with the descriptions of max-min segments, semispaces, hyperplanes and an account of separation and non-separation results based on semispaces. There are some new results. In particular, we give new "colorful" extensions of the max-min Caratheodory theorem. In the end of the paper, we list some consequences of the topological Radon and Tverberg theorems (like Helly and Centerpoint theorems), valid over a more general class of max-T semirings, where multiplication is a triangular norm.

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Viorel Nitica, Sergei Sergeev. 2013-03-29. Tropical convexity over max-min semiring. https://arxiv.org/abs/1303.7451

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