# Optimal bounds for the colored Tverberg problem

Pavle V. M. Blagojević; Benjamin Matschke; Günter M. Ziegler

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 4, page 739-754
- ISSN: 1435-9855

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topBlagojević, Pavle V. M., Matschke, Benjamin, and Ziegler, Günter M.. "Optimal bounds for the colored Tverberg problem." Journal of the European Mathematical Society 017.4 (2015): 739-754. <http://eudml.org/doc/277250>.

@article{Blagojević2015,

abstract = {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 Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & 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.},

author = {Blagojević, Pavle V. M., Matschke, Benjamin, Ziegler, Günter M.},

journal = {Journal of the European Mathematical Society},

keywords = {optimal colored Tverberg theorem; Bárány–Larman conjecture; equivariant obstruction theory; chessboard complexes; optimal colored Tverberg theorem; Barany-Larman conjecture; equivariant obstruction theory; chessboard complexes},

language = {eng},

number = {4},

pages = {739-754},

publisher = {European Mathematical Society Publishing House},

title = {Optimal bounds for the colored Tverberg problem},

url = {http://eudml.org/doc/277250},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Blagojević, Pavle V. M.

AU - Matschke, Benjamin

AU - Ziegler, Günter M.

TI - Optimal bounds for the colored Tverberg problem

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 4

SP - 739

EP - 754

AB - 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 Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & 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.

LA - eng

KW - optimal colored Tverberg theorem; Bárány–Larman conjecture; equivariant obstruction theory; chessboard complexes; optimal colored Tverberg theorem; Barany-Larman conjecture; equivariant obstruction theory; chessboard complexes

UR - http://eudml.org/doc/277250

ER -

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