Equal coefficients and tolerance in coloured tverberg partitions

The coloured Tverberg theorem was conjectured by Barany, Lovasz and Furedi [2] and asks whether for any d+1 sets (considered as colour classes) of k points each in Rd there is a partition of them into k colourful sets whose convex hulls intersect. This is known when d=1,2 [3] or k+1 is prime [5]. In this paper we show that (k-1)d+1 colour classes are… CONTINUE READING

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