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A partition property of simplices in Euclidean space

Authors: P. Frankl and V. Rödl
Journal: J. Amer. Math. Soc. 3 (1990), 1-7
MSC: Primary 52A37; Secondary 05A99
MathSciNet review: 1020148
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Abstract: Given the vertex set $ A$ of a nondegenerate simplex in $ {R^d}$, it is shown that for some positive $ \varepsilon = \varepsilon (A)$ and every partition of $ {R^n}$ into fewer than $ {(1 + \varepsilon )^n}$ parts, one of the parts must contain a set congruent to $ A$. This solves a fifteen-year-old problem of Erdös et al. [E].

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Article copyright: © Copyright 1990 American Mathematical Society

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