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Primitive Radon partitions

Published online by Cambridge University Press:  26 February 2010

J. Eckhoff
Affiliation:
Mathematisches Institut, Universität DOrtmund, Dortmund, Germany
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Extract

Radon's theorem [8] asserts that, if X is a finite set of s points in Rd and s ≥ d + 2, then X admits a. Radon partition, that is, a partition {X1; X2} of X into disjoint subsets X1 and X2, such that

Type
Research Article
Copyright
Copyright © University College London 1974

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References

1.Breen, M.. “A determination of the combinatorial type of a polytope by Radon partitions”, Ph.D. Thesis (Clemson Univ., 1970).Google Scholar
2.Breen, M.. “Determining a polytope by Radon partitions”, Pacific J. Math., 43 (1972), 2737.CrossRefGoogle Scholar
3.Eckhoff, J.. “Der Satz von Radon in konvexen Produktstrukturen I I”, Monatsh. Math., 73 (1969), 730.CrossRefGoogle Scholar
4.Eckhoff, J.. “Radonpartitionen und konvexe Polyeder”, j. reine angew. Math., to appear.Google Scholar
5.Grünbaum, B.. Convex polytopes (London–New York–Sydney, 1967).Google Scholar
6.Hare, W. R. and Kenelly, J. W.. “Characterization of Radon partitions”, Pacific J. Math., 36 (1971), 159164.CrossRefGoogle Scholar
7.McMullen, P.. “The numbers of faces of simplicial polytopes”, Israel J. Math., 9(1971), 559570.CrossRefGoogle Scholar
8.Radon, J.. “Mengen konvexer Korper, die einen gemeinsamen Punkt enthalten”, Math. Ann., 83(1921), 113115.CrossRefGoogle Scholar
9.Shephard, G. C.. “Neighbourliness and Radon's theorem”, Mathematika, 16 (1969), 273275.CrossRefGoogle Scholar