## Reay has conjectured that any set of (m -l)(d + 1) + k + 1 points in general position in Rd can be partitioned into m disjoint subsets S,, S,, ,
Optimum partitioning into intersections of ring families
✍ Scribed by Maurice Cochand; Arlette Gaillard; Heinz Gröflin
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 680 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0166-218X
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📜 SIMILAR VOLUMES
Tverberg's 1966 theorem asserts that every set X of (m -1)(d + 1) + 1 points in R d has a partition X 1 , X 2 , . . . , X m such that m i=1 conv X i = φ. We give a short and elementary proof of a theorem on convex cones which generalizes this result. As a consequence, we deduce several divisibility
A longstanding conjecture of Reay asserts that every set X of (m-1)(d +1)+k+1 points in general position in R d has a partition X 1 , X 2 , . . . , X m such that m i=1 conv X i is at least k-dimensional. Using the tools developed in [13] and oriented matroid theory, we prove this conjecture for d =
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