Geometric & Functional Analysis GAFA

, Volume 13, Issue 3, pp 467–482

Equilateral Sets in lpn

Original Article

DOI: 10.1007/s00039-003-0418-7

Cite this article as:
Alon, N. & Pudlák, P. Geom. funct. anal. (2003) 13: 467. doi:10.1007/s00039-003-0418-7

Abstract

We show that for every odd integer p ≥1 there is an absolute positive constantcp, so that the maximum cardinality of a set of vectors in Rn such that the lp distance between any pair is precisely 1, is at most cpn log n. We prove some upper bounds for other lp norms as well.

Keywords.

((no keywords))

Copyright information

© Birkhäuser-Verlag 2003

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrinceton UniversityPrincetonUSA
  2. 2.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  3. 3.Mathematical InstituteAcademy of Sciences of the Czech RepublicPragueCzech Republic