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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
172 Combinatorics of Permutations, Second Edition.
that all their ancestors have a positive label. If that happens, we resort to the
following proposition to locate the vertex associated with n.
PROPOSITION 4.51
Suppose p
n
= n.Thenn is the leftmost entry of p that has the property that
each of its ancestors (including itself ) has a positive label.
PROOF Suppose p
k
and n both have this property and that p
k
is on
the left of n. (If there are several candidates for the role of p
k
, choose the
rightmost one). If p
k
beats an element y on the right of n by participating in
the 132-pattern xp
k
y,thenxp
k
ny is a 1342-pattern, which is a contradiction.
So p
k
does
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Publisher Resources

ISBN: 9781439850527