Barany, I;
Soberon, P;
(2018)
Tverberg Plus Minus.
Discrete & Computational Geometry
, 60
(3)
pp. 588-598.
10.1007/s00454-017-9960-1.
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Abstract
We prove a Tverberg type theorem: Given a set A ⊂ R d in general position with |A| = (r − 1)(d + 1) + 1 and k ∈ {0, 1, . . . , r − 1}, there is a partition of A into r sets A1, . . . , Ar (where |Aj | ≤ d + 1 for each j) with the following property. There is a unique z ∈ Tr j=1 aff Aj and it can be written as an affine combination of the element in Aj : z = P x∈Aj α(x)x for every j and exactly k of the coefficients α(x) are negative. The case k = 0 is Tverberg’s classical theorem.
| Type: | Article |
|---|---|
| Title: | Tverberg Plus Minus |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00454-017-9960-1 |
| Publisher version: | https://doi.org/10.1007/s00454-017-9960-1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Tverberg’s theorem, Sign conditions |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/1534227 |
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