Albert, M. H.; Atkinson, M. D. and Brignall, Robert
Permutation Classes of Polynomial Growth.
Annals of Combinatorics, 11(3-4) pp. 249–264.
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.
Actions (login may be required)