Permutation Classes of Polynomial Growth
Combinatorics
2007-05-23 v2
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.
Cite
@article{arxiv.math/0603315,
title = {Permutation Classes of Polynomial Growth},
author = {M. H. Albert and M. D. Atkinson and Robert Brignall},
journal= {arXiv preprint arXiv:math/0603315},
year = {2007}
}
Comments
17 pages, 4 figures