Summary: Permutation Classes of Polynomial Growth
M. H. Albert
, M. D. Atkinson
Department of Computer Science
University of Otago, Dunedin, New Zealand
Department of Mathematics and Statistics
St Andrews, UK.
May 15, 2007
A pattern class is a set of permutations closed under the formation
of subpermutations. Such classes can be characterised as those permuta-
tions not involving a particular set of forbidden permutations. A simple
collection of necessary and sufficient conditions on sets of forbidden per-
mutations which ensure that the associated pattern class is of polynomial
growth is determined. A catalogue of all such sets of forbidden permuta-
tions having three or fewer elements is provided together with bounds on
the degrees of the associated enumerating polynomials.