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Tverberg Plus Minus

Barany, I; Soberon, P; (2018) Tverberg Plus Minus. Discrete & Computational Geometry , 60 (3) pp. 588-598. 10.1007/s00454-017-9960-1. Green open access

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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.ucl.ac.uk/id/eprint/1534227
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