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

DOI:
https://doi.org/10.1090/S0894-0347-1990-1020148-2

MathSciNet review:
1020148

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Abstract: Given the vertex set of a nondegenerate simplex in , it is shown that for some positive and every partition of into fewer than parts, one of the parts must contain a set congruent to . This solves a fifteen-year-old problem of Erdös et al. [E].

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DOI:
https://doi.org/10.1090/S0894-0347-1990-1020148-2

Article copyright:
© Copyright 1990
American Mathematical Society