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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
38 Combinatorics of Permutations, Second Edition
2
1
2
1
3
3
FIGURE 1.10
The two decreasing non-plane trees on vertex set [3].
13. We say that i is a weak excedance of p = p
1
p
2
···p
n
if p
i
i. Assuming
Theorem 1.36, prove that the number of n-permutations with k weak
excedances is A(n, k).
14. Prove that for all positive integers n,wehave
S(n +1,k+1)=
n
m=k
n
m
S(m, k).
15. A decreasing non-plane tree is a rooted tree on vertex set [n]inwhich
each non-leaf vertex has at most two children, and the label of each
vertex is smaller than that of its parent. See Figure 1.10 for the two
decreasing non-plane trees on vertex set [3]. Let T
n
denote the number
of decreasing ...
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Publisher Resources

ISBN: 9781439850527