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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
280 Combinatorics of Permutations, Second Edition
anywhere before position j +1.
On the other hand, x cannot enter the first row anywhere after position j+1
either. Indeed, assume this happens; this implies that when x starts looking
for a position, there is an entry y<xin position j +1ofthe firstrow. By
our induction hypothesis, that entry cannot have rank less than j +1. That
is a contradiction, however, for we could affix x to the end of any increasing
subsequence ending in y, yielding that the rank of x is at least j +2.
The result of Lemma 7.3 provides an obvious alternative proof of the fact
that S
n
(123 ···k) (k 1)
2n
. There is, however, a muc
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Publisher Resources

ISBN: 9781439850527