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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
270 Combinatorics of Permutations, Second Edition
4. Let us keep the notation of the solution of Problem Plus 2. Furthermore,
let us introduce the new notation
e
λ
=
hjkl
a
i
(a
j
1)(a
k
2)(a
l
3)
n(n 1)(n 2)(n 3)
.
It is then proved in [169] that
E(X
i,j
)=c
λ
d
λ
d
λ
+ e
λ
+ e
λ
,
where c
λ
is defined in (6.25) below.
5. This probability converges to zero as n goes to infinity as is proved in
[96].
6. This probability converges to 1 as n goes to infinity as is shown in [138].
7. Let the given shape λ have rows of length a
1
,a
2
, ···,a
k
and columns of
length a
1
,a
2
, ···,a
k
. It then follows from a more general result of Peter
ast¨o [169] that
c
λ
= E
d,λ
=
n 1
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Publisher Resources

ISBN: 9781439850527