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Stirling numbers of the
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Permutations
Definition 5.6.1
A
permutation
of a set
is a bijection
.
For the set
, the notation
denotes the permutation
of
such that
,
, etc.
Definition 5.6.2
Let
be a set and
be a subset of
. Let
be a permutation of
verifying the following properties:
(i)
,
, ...,
(renumbering the elements of
if necessary;
(ii)
for any
,
.
Then
is called a
cycle
.
For example, in
is a cycle, whose notation can be shortened to
.
Proposition 5.6.3
Any permutation is the product of disjoint cycles.
Subsections
Stirling numbers of the first kind
Transpositions and shuffles
Order of a permutation
Conjugacy classes in
root 2002-06-10