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Inscribed Tverberg-Type Partitions for Orbit Polytopes
[article]

2022
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arXiv
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pre-print

Tverberg's theorem states that any set of t(r,d)=(r-1)(d+1)+1 points in ℝ^d can be partitioned into r subsets whose convex hulls have non-empty r-fold intersection. Moreover, generic collections of fewer points cannot be so divided. Extending earlier work of the first author, we show that one can nonetheless guarantee inscribed "polytopal partitions" with specified symmetry conditions in many such circumstances. Namely, for any faithful and full–dimensional orthogonal representation ρ G→ O(d)

arXiv:2110.09322v3
fatcat:xw2mr5yuxneulp7gs5wotdlcty