, Volume 11, Issue 3-4, pp 249-264

Permutation Classes of Polynomial Growth

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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.

Received March 14, 2006