Projective Center Point and Tverberg Theorems

We present projective versions of the center point theorem and Tverberg’s theorem, interpolating between the original and the so-called “dual” center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) T...

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Bibliographic Details
Published in:Discrete & computational geometry 2014-07, Vol.52 (1), p.88-101
Main Authors: Karasev, Roman, Matschke, Benjamin
Format: Article
Language:English
Subjects:
Combinatorics
Computational geometry
Computational Mathematics and Numerical Analysis
Geometry
Mathematics
Mathematics and Statistics
Partitioning
Theorems
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Summary:We present projective versions of the center point theorem and Tverberg’s theorem, interpolating between the original and the so-called “dual” center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-014-9602-9