Exact enumeration of 1342-avoiding permutations: a close link with labeled trees and planar maps
Journal of Combinatorial Theory Series A
Discrete Mathematics
Restricted permutations and the wreath product
Discrete Mathematics
Embedding dualities for set partitions and for relational structures
European Journal of Combinatorics
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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, contiguity and subrepresentations for classes admitting multiple representations of this form.