Combinatorial Gray codes for classes of pattern avoiding permutations

W. M.B. Dukes, M. F. Flanagan, T. Mansour, V. Vajnovszki

Research output: Contribution to journalArticlepeer-review


The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoiding permutations. Among the families under consideration are those counted by Catalan, large Schröder, Pell, even-index Fibonacci numbers and the central binomial coefficients. We thus provide Gray codes for the set of all permutations of {1, ..., n} avoiding the pattern τ for all τ ∈ S3 and the Gray codes we obtain have distances 4 or 5.

Original languageEnglish
Pages (from-to)35-49
Number of pages15
JournalTheoretical Computer Science
Issue number1-3
StatePublished - 10 May 2008


  • Generating algorithms
  • Gray codes
  • Pattern avoiding permutations

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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