Tverberg's theorem with constraints
| dc.creator | Hell, Stephan | |
| dc.date | 2007-04-20 | |
| dc.date | 2008-02-25 | |
| dc.date.accessioned | 2026-07-07T09:22:41Z | |
| dc.date.available | 2026-07-07T09:22:41Z | |
| dc.description | The topological Tverberg theorem claims that for any continuous map of the (q-1)(d+1)-simplex to R^d there are q disjoint faces such that their images have a non-empty intersection. This has been proved for affine maps, and if $q$ is a prime power, but not in general. We extend the topological Tverberg theorem in the following way: Pairs of vertices are forced to end up in different faces. This leads to the concept of constraint graphs. In Tverberg's theorem with constraints, we come up with a list of constraints graphs for the topological Tverberg theorem. The proof is based on connectivity results of chessboard-type complexes. Moreover, Tverberg's theorem with constraints implies new lower bounds for the number of Tverberg partitions. As a consequence, we prove Sierksma's conjecture for $d=2$, and $q=3$. | |
| dc.description | 16 pages, 12 figures. Accepted for publication in JCTA. Substantial revision due to the referees | |
| dc.identifier | https://arxiv.org/abs/0704.2713 | |
| dc.identifier | http://arxiv.org/abs/0704.2713 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155461 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A18; 52A37 | |
| dc.title | Tverberg's theorem with constraints | |
| dc.type | text |