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ALMOST ALL SETS OF $d+ 2$ POINTS ON THE $(d- 1)$ -SPHERE ARE NOT SUBTRANSITIVE

  • Sean Eberhard (a1)

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} $ .

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1.Frankl, P. and Rödl, V., A partition property of simplices in Euclidean space. J. Amer. Math. Soc. 3 (1) (1990), 17.
2.Johnson, F. E. A., Finite subtransitive sets. Math. Proc. Cambridge Philos. Soc. 140 (2006).
3.Leader, I., Russell, P. A. and Walters, M., Transitive sets and cyclic quadrilaterals. J. Comb. 2 (3) (2011), 457462.
4.Leader, I., Russell, P. A. and Walters, M., Transitive sets in Euclidean Ramsey theory. J. Combin. Theory Ser. A 119 (2) (2012), 382396.
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ALMOST ALL SETS OF $d+ 2$ POINTS ON THE $(d- 1)$ -SPHERE ARE NOT SUBTRANSITIVE

  • Sean Eberhard (a1)

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