Geodesic
A partition property of simplices in Euclidean space
Journal of the American Mathematical Society, Tome 03 (1990) no. 1, pp. 1-7

Voir la notice de l'article provenant de la source American Mathematical Society

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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Frankl, P.; Rödl, V. A partition property of simplices in Euclidean space. Journal of the American Mathematical Society, Tome 03 (1990) no. 1, pp. 1-7. doi: 10.1090/S0894-0347-1990-1020148-2

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