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Permutation Classes of Polynomial Growth
M.H. Albert1, M.D. Atkinson1, and Robert Brignall2
1Department of Computer Science, University of Otago, PO Box 56, Dunedin, New Zealand
{malbert, mike}@cs.otago.ac.nz
2Department of Mathematics and Statistics, University of St Andrews, St Andrews, Fife KY16 9AG, Scotland
robertb@mcs.st-and.ac.uk
Annals of Combinatorics 11 (3-4) p.249-264 September, 2007
AMS Subject Classification: 05A15, 05A05
Abstract:
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterized as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and sufficient conditions on sets of forbidden permutations which ensure that the associated pattern class is of polynomial growth is determined. A catalogue of all such sets of forbidden permutations having three or fewer elements is provided together with bounds on the degrees of the associated enumerating polynomials.
Keywords: restricted permutations, pattern avoidance, growth rate, polynomial growth

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