Pattern classes of permutations via bijections between linearly ordered sets

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3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)118-139
Number of pages22
JournalEuropean Journal of Combinatorics
Volume29
Issue number1
Early online date20 Jan 2007
DOIs
Publication statusPublished - Jan 2008

Keywords

  • Restricted permutations

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