05279822

j

05279822 Dukes, W.M.B. Flanagan, M.F. Mansour, T. Vajnovszki, V. Combinatorial Gray codes for classes of pattern avoiding permutations. Theor. Comput. Sci. 396, No. 1-3, 35-49 (2008). 2008 Elsevier Science Publishers, Amsterdam EN Gray codes pattern avoiding permutations generating algorithms

doi:10.1016/j.tcs.2007.12.002

Summary: 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 Schr\"oder, Pell, even-index Fibonacci numbers and the central binomial coefficients. We thus provide Gray codes for the set of all permutations of $\{1,\cdots ,n\}$ avoiding the pattern $\tau $ for all $\tau \in \frak S_3$ and the Gray codes we obtain have distances 4 or 5.