Pattern classes of permutations via bijections between linearly ordered sets
Abstract
A pattern class is a set of permutations closed under pattern involvement or, equivalently, defined by certain subsequence avoidance conditions. Any pattern class X which is atomic, i.e. indecomposable as a union of proper subclasses, has a representation as the set of subpermutations of a bijection between two countable (or finite) linearly ordered sets A and B. Concentrating on the situation where A is arbitrary and B = N, we demonstrate how the order-theoretic properties of A determine the structure of X and we establish results about independence, contiguousness and subrepresentations for classes admitting multiple representations of this form.
Citation
Huczynska , S & Ruskuc , N 2008 , ' Pattern classes of permutations via bijections between linearly ordered sets ' , European Journal of Combinatorics , vol. 29 , no. 1 , pp. 118-139 . https://doi.org/10.1016/j.ejc.2006.12.005
Publication
European Journal of Combinatorics
Status
Peer reviewed
ISSN
0195-6698Type
Journal article
Rights
This is an author version of this article. The published version (c) 2007 Elsevier Ltd. is available from www.sciencedirect.com
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.