Skip to Main Content
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
328 Combinatorics of Permutations, Second Edition
1
2
3
4
5
67
8
8
7
4
56
3
2
1
8
47
6
5
13
2
FIGURE 8.4
A decreasing binary tree and its image under z.
Take the sequence T
1
,T
2
, ···,T
n
. Denote by (T ) the number of left edges of
the forest T ,andbyr(T ) the number of right edges of the forest T .Findthe
smallest index i so that (T
i
) r(T
i
) = 1. We will now explain why such an
index always exists. If T
2
is a left edge, then (T
2
) r(T
2
)=1 0 = 1, and
we are done. Otherwise, at the beginning we have (T
2
) r(T
2
) < 1, while at
the end we have
(T
n
) r(T
n
) > ((n 1) −(n 3)/2) −(n 3)/2 > 1,
because of the restriction on k. So at the beginning, (T
j
)r(T
j
) is too ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Introduction to Combinatorics, 2nd Edition

Introduction to Combinatorics, 2nd Edition

Martin J. Erickson

Publisher Resources

ISBN: 9781439850527