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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
68 Combinatorics of Permutations, Second Edition
2.2 Inversions in Permutations of Multisets
Instead of permuting the elements of our favorite set, [n], in this section
we are going to permute elements of multisets. We will use the notation
{1
a
1
, 2
a
2
, ···,k
a
k
} for the multiset consisting of a
i
copies of i, for all i [k].
For our purposes, a permutation of a multiset is just a way of listing all its
elements. It is straightforward to see, and is proved in most undergraduate
textbooks on enumerative combinatorics, that the number of all permutations
of the multiset K = {1
a
1
, 2
a
2
, ···,k
a
k
} is
n!
a
1
!a
2
! ···a
k
!
,
where n = a
1
+ a
2
+ ···+ a
k
.
An inversion of
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Publisher Resources

ISBN: 9781439850527