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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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A partition property of simplices in Euclidean space
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by P. Frankl and V. Rödl PDF
J. Amer. Math. Soc. 3 (1990), 1-7 Request permission

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].
References
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • 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