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Permutation Classes of Polynomial Growth

M. H. Albert·M. D. Atkinson·Robert Brignall
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Abstract

A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised 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.

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M. H. Albert, M. D. Atkinson, Robert Brignall. 2007-02-07. Permutation Classes of Polynomial Growth. https://arxiv.org/abs/math/0603315

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