Annals of Combinatorics

, Volume 11, Issue 3–4, pp 249–264 | Cite as

Permutation Classes of Polynomial Growth



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.

AMS Subject Classification:

05A15 05A05 


restricted permutations pattern avoidance growth rate polynomial growth 


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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  • M. H. Albert
    • 1
  • M. D. Atkinson
    • 1
  • Robert Brignall
    • 2
  1. 1.Department of Computer ScienceUniversity of OtagoDunedinNew Zealand
  2. 2.Department of Mathematics and StatisticsUniversity of St AndrewsSt Andrews, FifeScotland

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