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A combinatorial perspective on the Radon convexity theorem

✍ Scribed by T. H. Brylawski

Publisher
Springer
Year
1976
Tongue
English
Weight
324 KB
Volume
5
Category
Article
ISSN
0046-5755

No coin nor oath required. For personal study only.

✦ Synopsis

Matroid-theoretic methods are employed to compute the number of complementary subsets of points of a set S whose convex hulls intersect (a number Radon proved to be nonzero when S has an affme dependency). This number is shown to be an invariant only of the dependence structure of S. Strict bounds are given depending on the cardinality and dimension of S and the number is related to other matroid invariants.

πŸ“œ SIMILAR VOLUMES

On Generalizations of Radon's Theorem an
On Generalizations of Radon's Theorem and the Ham Sandwich Theorem
✍ Helge Tverberg; SiniΕ‘a VreΔ‡ica πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 211 KB

We raise a conjecture which would generalize Radon's theorem and would provide combinatorial proof for the result from [7], which generalizes Rado's theorem on general measure and the Ham sandwich theorem. We prove that the conjecture holds in several particular cases.

On injectivity of the combinatorial Rado
On injectivity of the combinatorial Radon transform of order five
✍ Tewodros Amdeberhan; Melkamu Zeleke πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 183 KB

In the present work, we give a proof of the injectivity of the combinatorial Radon transform of order five.