Analogues of the central point theorem for families with $d$-intersection property in $\mathbb R^d$
Abstract
In this paper we consider families of compact convex sets in $\mathbb R^d$ such that any subfamily of size at most $d$ has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg's theorem for such families.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2009
- DOI:
- 10.48550/arXiv.0906.2262
- arXiv:
- arXiv:0906.2262
- Bibcode:
- 2009arXiv0906.2262K
- Keywords:
-
- Mathematics - Metric Geometry;
- Mathematics - Combinatorics;
- 52A20;
- 52A35;
- 52C35
- E-Print:
- Combinatorica 32:6 (2012), 689-702