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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
410 Combinatorics of Permutations, Second Edition
FIGURE 10.4
A 1-2 tree.
15. As a 132-avoiding permutation is indecomposable if and only if it ends
with its largest entry, the number of such k-permutations is C
k1
.Let
our three blocks end in positions i, j,andn. With these restrictions, we
clearly have C
i1
C
ji1
C
nj1
permutations with the desired property.
Now we have to sum this expression for all possible i and j to get
the total number of 132-avoiding n-permutations having exactly three
blocks. We do this in two steps. First, fix i, and compute the sum
C
i1
n1
j=i+1
C
ji1
C
nj1
= C
i1
C
ni1
.
Second, we sum over all possible i togetthatthereexist
n
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Publisher Resources

ISBN: 9781439850527