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ON EMBEDDINGS OF FINITE METRIC SPACES IN ln∞

Part of: Graph theory General convexity

Published online by Cambridge University Press:  10 December 2009

F. V. Petrov ,
D. M. Stolyarov  and
P. B. Zatitskiy
F. V. Petrov
Affiliation:
St. Petersburg Department of Steklov Mathematical Institute RAS 27, Fontanka, 191023 St. Petersburg, Russia
D. M. Stolyarov
Affiliation:
Saint-Petersburg State University, Mathematics and Mechanics Faculty, Universitetsky prospekt, 28, 198504, St. Petersburg, Russia
P. B. Zatitskiy
Affiliation:
Saint-Petersburg State University, Mathematics and Mechanics Faculty, Universitetsky prospekt, 28, 198504, St. Petersburg, Russia
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Abstract

We prove that for any given integer c≥0 any metric space on n points may be isometrically embedded into ln−c∞ provided n is large enough.

MSC classification

Secondary: 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.) 05C55: Generalized Ramsey theory
Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 135 - 139
Copyright
Copyright © University College London 2010

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References

[1]Alon, N., Eigenvalues, geometric expanders, sorting in rounds, and Ramsey theory. Combinatorica 6(3) (1986), 207–219.CrossRefGoogle Scholar
[2]Averkov, G. and Düvelmeyer, N., Embedding metric spaces into normed spaces and estimates of metric capacity. Monatsh. Math. 152(3) (2007), 197–206.CrossRefGoogle Scholar
[3]Ball, K., Isometric embedding in lp-spaces. European J. Combin. 11(4) (1990), 305–311.Google Scholar
[4]Spencer, J., Asymptotic lower bounds for Ramsey functions. Discrete Math. 20(1) (1977/78), 69–76.Google Scholar
[5]Wolfe, D., Imbedding a finite metric set in an N-dimensional Minkowski space. Nederl. Akad. Wetensch. Proc. Ser. A 70 (1967), 136–140.CrossRefGoogle Scholar