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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Received March 14, 2006
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Albert, M.H., Atkinson, M.D. & Brignall, R. Permutation Classes of Polynomial Growth. Ann. Comb. 11, 249–264 (2007). https://doi.org/10.1007/s00026-007-0318-x
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DOI: https://doi.org/10.1007/s00026-007-0318-x