Optimal bounds for the colored Tverberg problem

By Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler. 2009

105 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/cf0afd6022b5d1aa7faf77e7ab3fef2a42c9e5d1

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In Computational Theory and Mathematics

1. Florian Frick
2. Pavle V. M. Blagojević
3. Günter M. Ziegler
4. Jirí Matousek

In Computer Graphics and Computer-Aided Design

1. Florian Frick
2. Pavle V. M. Blagojević
3. Günter M. Ziegler

In Computer Vision and Pattern Recognition

1. Florian Frick
2. Pavle V. M. Blagojević
3. Günter M. Ziegler

Citations in the corpus

• Tverberg plus constraints (2014, methodology): “he upper bound of ˇZivaljevi´c and Vre´cica on the function tt(d,r) does not provide any information about the function n(d,r) of B´arany and Larman. Only recently Blagojevi´c, Matschke & Ziegler [7], as a consequence of their “optimal colored Tverberg theorem”, established that n(d,r) = r(d +1)”