Combinatorial Gray codes for classes of pattern avoiding permutations

Authors:
W. M. B. Dukes;M. F. Flanagan;T. Mansour;V. Vajnovszki
Affiliations:
Science Institute, University of Iceland, Reykjavík, Iceland;Institute for Digital Communications, The University of Edinburgh, The Kings Buildings, Mayfield Road, Edinburgh EH9 3JL, Scotland, United Kingdom;Department of Mathematics, University of Haifa, 31905 Haifa, Israel;LE2I UMR CNRS 5158, Université de Bourgogne B.P. 47 870, 21078 DIJON-Cedex, France
Venue:
Theoretical Computer Science
Year:
2008

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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, large Schroder, Pell, even-index Fibonacci numbers and the central binomial coefficients. We thus provide Gray codes for the set of all permutations of {1,...,n} avoiding the pattern @t for all @t@?S"3 and the Gray codes we obtain have distances 4 or 5.