Bárány, Imre and Pach, János (2014) Homogeneous selections from hyperplanes. JOURNAL OF COMBINATORIAL THEORY SERIES B, 104. pp. 81-87. ISSN 0095-8956
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Abstract
Given d + 1 hyperplanes h1, ..., hd + 1 in general position in Rd, let △ (h1, ..., hd + 1) denote the unique bounded simplex enclosed by them. There exists a constant c (d) > 0 such that for any finite families H1, ..., Hd + 1 of hyperplanes in Rd, there are subfamilies Hi * ⊂ Hi with | Hi * | ≥ c (d) | Hi | and a point p ∈ Rd with the property that p ∈ △ (h1, ..., hd + 1) for all hi ∈ Hi *. © 2013 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Intersecting simplices; Hyperplanes; hypergraphs |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 18 Feb 2015 14:51 |
| Last Modified: | 18 Feb 2015 14:51 |
| URI: | http://real.mtak.hu/id/eprint/21926 |
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