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A partition property of simplices in Euclidean space
P. Frankl, V. Rödl
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Source: Crossref
Published: Jan 1, 1990
DOI: 10.1090/s0894-0347-1990-1020148-2
Open original source ↗Source abstract
Given the vertex set A A of a nondegenerate simplex in R d {R^d} , it is shown that for some positive ε = ε ( A ) \varepsilon = \varepsilon (A) and every partition of R n {R^n} into fewer than ( 1 + ε ) n {(1 + \varepsilon )^n} parts, one of the parts must contain a set congruent to A A . This solves a fifteen-year-old problem of Erdös et al. [E].
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