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Combinatorics of Permutations, 2nd Edition
book

Combinatorics of Permutations, 2nd Edition

by Miklos Bona
April 2016
Intermediate to advanced content levelIntermediate to advanced
478 pages
14h 44m
English
Chapman and Hall/CRC
Content preview from Combinatorics of Permutations, 2nd Edition
4
In Any Way but This. Pattern Avoidance.
The Basics.
4.1 The Notion of Pattern Avoidance
In earlier chapters, we have studied inversions of permutations. These were
pairs of elements that could be anywhere in the permutation, but always
related to each other the same way, that is, the one on the left was always
larger.
There is a far-fetching generalization of this notion from pairs of entries to
k-tuples of entries. Consider a “long” permutation, such as p = 25641387,
and a shorter one, say q = 132. We then say that the 3-tuple of entries (2,6,4)
in p forms a pattern or subsequence of type 132 because the entries (2,6,4) of
p relate to each other as
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Publisher Resources

ISBN: 9781439850527