Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-13T07:26:50.082Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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