Original Article

Geometric & Functional Analysis GAFA

, Volume 13, Issue 3, pp 467-482

First online:

Equilateral Sets in l p n

  • Noga AlonAffiliated withInstitute for Advanced Study, Princeton UniversitySchool of Mathematical Sciences, Tel Aviv University Email author 
  • , Pavel PudlákAffiliated withMathematical Institute, Academy of Sciences of the Czech Republic

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Abstract

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

Keywords.

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