Tverberg Plus Minus

Bárány, Imre and Soberón, P. (2018) Tverberg Plus Minus. DISCRETE AND COMPUTATIONAL GEOMETRY, 60 (3). pp. 588-598. ISSN 0179-5376

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Abstract

We prove a Tverberg type theorem: Given a set A Rd 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 zj=1raffAj and it can be written as an affine combination of the element in Aj: z=∑x∈Ajα(x)x for every j and exactly k of the coefficients α(x) are negative. The case k= 0 is Tverberg’s classical theorem. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

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