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Bounding the Number of Geometric Permutations Induced byk-Transversals

✍ Scribed by Jacob E. Goodman; Richard Pollack; Rephael Wenger

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 352 KB
Volume: 75
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.1996.0072

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that a suitably separated family of n compact convex sets in R d can be met by k-flat transversals in at most d&k) , or for fixed k and d, O(n k(k+1)(d&k) ) different order types. This is the first non-trivial upper bound for 12.

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