Automorphic subsets of the n-dimensional cube

Gareth Jones, Mikhail Klin, Felix Lazebnik

Research output: Contribution to journalArticlepeer-review


An automorphic subset of the n-dimensional cube Qn is an orbit of a subgroup of Aut(Qn), acting on the vertices. We develop a theory of such subsets, and we show that those containing 0 coincide with the cwatsets introduced by Sherman and Wattenberg in response to a statistical result of Hartigan. Using this characterisation, together with results from finite group theory and number theory, we answer two questions on cwatsets posed by Sherman and Wattenberg, and we complete the proofs of some results outlined by Kerr.

Original languageEnglish
Pages (from-to)303-323
Number of pages21
JournalBeitrage zur Algebra und Geometrie
Issue number2
StatePublished - 1 Dec 2000


  • Automorphic subset
  • Cwatset
  • Hamming distance
  • Permutation group
  • Subgraph
  • Wreath product
  • n-dimensional cube

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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