Combinatorial Gray codes for classes of pattern avoiding permutations

W. M. B. Dukes, Mark Flanagan, Toufik Mansour, Vincent Vajnovszki

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Abstract

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, Schr\"oder, Pell, even index Fibonacci numbers and the central binomial coefficients. Consequently, this provides Gray codes for $\s_n(\tau)$ for all $\tau\in \s_3$ and the obtained Gray codes have distances 4 and 5.
Original languageEnglish
Pages (from-to)35 - 49
Number of pages15
JournalTheoretical Computer Science
Volume396
Issue number1 - 3
Publication statusPublished - May 2008

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Dukes, W. M. B., Flanagan, M., Mansour, T., & Vajnovszki, V. (2008). Combinatorial Gray codes for classes of pattern avoiding permutations. Theoretical Computer Science, 396(1 - 3), 35 - 49.