Abstract
An embedding of an n-dimensional manifold M into R d is called k-neighborly if, for every k points on the embedded manifold, there is a hyperplane H in R d which supports the manifold precisely at these points. Micha A. Perles (Problems presented in Oberwolfach conference on "Convexity", [1982]) asked: What is the smallest dimension d(k,n) of the ambient space in which a k-neighborly n-dimensional manifold exists? We prove that d(k,n)≤2k(k-1)n. Related results and open problems are discussed.
Original language | English |
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Pages (from-to) | 319-324 |
Number of pages | 6 |
Journal | Discrete and Computational Geometry |
Volume | 40 |
Issue number | 3 |
DOIs | |
State | Published - Oct 2008 |
Keywords
- Continuous hashing
- Convex bodies
- Cyclic polytopes
- Neighborliness
- Polytopes