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Summary: On permutation pattern classes with two
restrictions only
M. D. Atkinson
Department of Computer Science
University of Otago
February 19, 2007
Abstract
Permutation pattern classes that are defined by avoiding two permu-
tations only and which contain only finitely many simple permutations
are characterized and their growth rates are determined.
1 Introduction
Permutation pattern classes are sets of permutations that are closed under tak-
ing subpermutations. A permutation = p1p2 · · · pm is a subpermutation of (or
is involved in) a permutation = s1s2 · · · sn if has a subsequence si1 si2 · · · sim
that is order isomorphic to (that is, p1p2 · · · pm and si1 si2 · · · sim are in the
same relative order). For example 312 is a subpermutation of 41532 because of
the subsequence 413. Notice that 123 is not a subpermutation of 41532 and we
say that 41532 avoids 123.
Permutation pattern classes can equivalently be defined as sets of permutations
which avoid certain forbidden subpermutations. In this case we normally use
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