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Summary: Avoiding consecutive patterns in permutations
R. E. L. Aldred
M. D. Atkinson
D. J. McCaughan
January 3, 2009
Abstract
The number of permutations that do not contain, as a factor (subword), a given
set of permutations is studied. A new treatment of the case = {12 · · · k} is
given and then some numerical data is presented for sets consisting of permuta-
tions of length at most 4. Some large sets of Wilf-equivalent permutations are also
given.
1 Introduction
The notion of one permutation being contained in another permutation generally
refers to having a subsequence that is order isomorphic to . In generalised pat-
tern containment extra conditions are stipulated relating to when terms of should be
adjacent in . The extreme case of this, which we call consecutive pattern contain-
ment, is when we require all the terms of to be consecutive: so is consecutively
contained in if has a factor that is order isomorphic to . For example 521643
contains 132 because of the factor 164.
A frequently studied problem in pattern containment is to enumerate the permutations
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