Tropical convexity over max-min semiring [unknown]

Viorel Nitica, Sergeĭ Sergeev
2014 Contemporary Mathematics   unpublished
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 Carathéodory theorem. In the end of the paper, we list some consequences of the topological Radon and Tverberg theorems (like Helly and Centerpoint theorems),
more » ... over a more general class of max-T semirings, where multiplication is a triangular norm.
doi:10.1090/conm/616/12301 fatcat:vsmxfbnlandkpe5sydthcxcdki