2007/04/16 by W. M. B. Dukes, Dukes, W. M. B., Mark F. Flanagan +5
Mathematics · #05A05 #05A15 #94B25 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A15 #msc:94B25
paper · pdf · doi:10.48550/arxiv.0704.2048
18 pages
arxiv created 2008/01/09 · arxiv updated 2009/12/01
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, Schröder, Pell, even index Fibonacci numbers and the central binomial coefficients. Consequently, this provides Gray codes for \sn(τ) for all τ∈ \s3 and the obtained Gray codes have distances 4 and 5.