Pythagorean powers of hypercubes

Assaf Naor, Gideon Schechtman

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


It is shown here that for every n ∈ ℕ, any embedding into L1 of the n-fold Pythagorean power of the n-dimensional Hamming cube incurs distortion that is at least a constant multiple of √n. This is achieved through the introduction of a new bi-Lipschitz invariant of metric spaces that is inspired by a linear inequality of Kwapień and Schütt (1989). The new metric invariant is evaluated here for L1, implying the above nonembeddability statement. Links to the Ribe program are discussed, as well as related open problems.

Original languageEnglish (US)
Pages (from-to)1093-1116
Number of pages24
JournalAnnales de l'Institut Fourier
Issue number3
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Geometry and Topology


  • Metric embeddings
  • Ribe program


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