6533b827fe1ef96bd1285be0

RESEARCH PRODUCT

Combinatorial Gray codes for classes of pattern avoiding permutations

Mark F. FlanaganVincent VajnovszkiToufik MansourW. M. B. Dukes

subject

Mathematics::CombinatoricsFibonacci numberPattern avoiding permutationsGeneral Computer ScienceOrder (ring theory)Generating algorithms94B25Gray codesCombinatorial algorithms05A05; 94B25; 05A15Theoretical Computer ScienceCombinatoricsSet (abstract data type)Constraint (information theory)Gray codePermutation05A05ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsMathematics - CombinatoricsCombinatorics (math.CO)05A15Binomial coefficientComputer Science(all)Mathematics

description

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.

yearjournalcountryeditionlanguage
2007-04-16Theoretical Computer Science
https://doi.org/10.1016/j.tcs.2007.12.002