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Combinatorial Gray codes for classes of pattern avoiding permutations

Dukes, W. M. B. and Flanagan, Mark and Mansour, Toufik and Vajnovszki, Vincent (2008) Combinatorial Gray codes for classes of pattern avoiding permutations. Theoretical Computer Science, 396 (1 - 3). 35 - 49. ISSN 0304-3975

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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.