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ALMOST ALL SETS OF 
$d+ 2$ POINTS ON THE 
$(d- 1)$-SPHERE ARE NOT SUBTRANSITIVE
Part of:Extremal combinatorics
Published online by Cambridge University Press: 28 March 2013
Abstract
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We generalise an argument of Leader, Russell, and Walters to show that almost all sets of 
$d+ 2$ points on the 
$(d- 1)$-sphere 
${S}^{d- 1} $ are not contained in a transitive set in some 
${\mathbf{R} }^{n} $.
MSC classification
Secondary:05D10: Ramsey theory
Information
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2013
References
Frankl, P. and Rödl, V., A partition property of simplices in Euclidean space. J. Amer. Math. Soc. 3 (1) (1990), 1–7.CrossRefGoogle Scholar
Johnson, F. E. A., Finite subtransitive sets. Math. Proc. Cambridge Philos. Soc. 140 (2006).CrossRefGoogle Scholar
Leader, I., Russell, P. A. and Walters, M., Transitive sets and cyclic quadrilaterals. J. Comb. 2 (3) (2011), 457–462.Google Scholar
Leader, I., Russell, P. A. and Walters, M., Transitive sets in Euclidean Ramsey theory. J. Combin. Theory Ser. A 119 (2) (2012), 382–396.CrossRefGoogle Scholar
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