Optimal bounds for the colored Tverberg problem

Details Optimal bounds for the colored Tverberg problem Optimal bounds for the colored Tverberg problem

2009-10-26

arxiv.org/abs/0910.4987v2

Mathematics

Combinatorics

11 pages, 3 figures; revised version with additional author, more general main result, additional references etc

Scientific paper

We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Barany et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Barany & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.

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