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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

Sean Eberhard
Sean Eberhard*
Affiliation:
Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, U.K. email [email protected]
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Abstract

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
Type
Research Article
Information
Mathematika , Volume 59 , Issue 2 , July 2013 , pp. 267 - 268
Copyright
Copyright © University College London 2013 

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References

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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