Permutation classes of polynomial growth

Albert, M. H.; Atkinson, M. D. and Brignall, Robert (2007). Permutation classes of polynomial growth. Annals of Combinatorics, 11(3-4) pp. 249–264.

DOI: https://doi.org/10.1007/s00026-007-0318-x

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.

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