Pattern classes of permutations via bijections between linearly ordered sets
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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, contiguousness and subrepresentations for classes admitting multiple representations of this form.
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 . DOI: 10.1016/j.ejc.2006.12.005
European Journal of Combinatorics
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