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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
Mean and Insensitive. Random Permutations. 265
18. Let X
n
be defined on the set of derangements of length n, and let X
n
(p)
be the number of cycles of p.Provethatforn 4, we have
(n 1)D(n 2)E(X
n2
+1)+(n 1)D(n 1)E(X
n1
)=D(n)E(X
n
).
19. Let Y
n
be defined on the set of derangements of length n, and let Y
n
(p)
be the size of the cycle containing the maximal entry of p.Finda
recurrence relation for E(Y
n
).
20. We know from Section 1.2 that for any fixed n, the sequence G(n, k)is
unimodal. Where is the peak of that sequence, that is, for which k is
G(n, k) maximal?
21. Let p and q be two randomly selected n-permutations, and let G
p,q
be
the graph defined in Problem ...
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Publisher Resources

ISBN: 9781439850527