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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Metric transforms and Euclidean embeddings
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by M. Deza and H. Maehara PDF
Trans. Amer. Math. Soc. 317 (1990), 661-671 Request permission

Abstract:

It is proved that if $0 \leqslant c \leqslant 0.72/n$ then for any $n$-point metric space $(X,d)$, the metric space $(X,{d^c})$ is isometrically embeddable into a Euclidean space. For $6$-point metric space, $c = \tfrac {1} {2}{\log _2}\tfrac {3} {2}$ is the largest exponent that guarantees the existence of isometric embeddings into a Euclidean space. Such largest exponent is also determined for all $n$-point graphs with "truncated distance".
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 317 (1990), 661-671
  • MSC: Primary 51K05
  • DOI: https://doi.org/10.1090/S0002-9947-1990-0974513-6
  • MathSciNet review: 974513