Identifier
- St000020: Permutations ⟶ ℤ
Values
[1] => 1
[1,2] => 1
[2,1] => 2
[1,2,3] => 1
[1,3,2] => 2
[2,1,3] => 3
[2,3,1] => 4
[3,1,2] => 5
[3,2,1] => 6
[1,2,3,4] => 1
[1,2,4,3] => 2
[1,3,2,4] => 3
[1,3,4,2] => 4
[1,4,2,3] => 5
[1,4,3,2] => 6
[2,1,3,4] => 7
[2,1,4,3] => 8
[2,3,1,4] => 9
[2,3,4,1] => 10
[2,4,1,3] => 11
[2,4,3,1] => 12
[3,1,2,4] => 13
[3,1,4,2] => 14
[3,2,1,4] => 15
[3,2,4,1] => 16
[3,4,1,2] => 17
[3,4,2,1] => 18
[4,1,2,3] => 19
[4,1,3,2] => 20
[4,2,1,3] => 21
[4,2,3,1] => 22
[4,3,1,2] => 23
[4,3,2,1] => 24
[1,2,3,4,5] => 1
[1,2,3,5,4] => 2
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 5
[1,2,5,4,3] => 6
[1,3,2,4,5] => 7
[1,3,2,5,4] => 8
[1,3,4,2,5] => 9
[1,3,4,5,2] => 10
[1,3,5,2,4] => 11
[1,3,5,4,2] => 12
[1,4,2,3,5] => 13
[1,4,2,5,3] => 14
[1,4,3,2,5] => 15
[1,4,3,5,2] => 16
[1,4,5,2,3] => 17
[1,4,5,3,2] => 18
[1,5,2,3,4] => 19
[1,5,2,4,3] => 20
[1,5,3,2,4] => 21
[1,5,3,4,2] => 22
[1,5,4,2,3] => 23
[1,5,4,3,2] => 24
[2,1,3,4,5] => 25
[2,1,3,5,4] => 26
[2,1,4,3,5] => 27
[2,1,4,5,3] => 28
[2,1,5,3,4] => 29
[2,1,5,4,3] => 30
[2,3,1,4,5] => 31
[2,3,1,5,4] => 32
[2,3,4,1,5] => 33
[2,3,4,5,1] => 34
[2,3,5,1,4] => 35
[2,3,5,4,1] => 36
[2,4,1,3,5] => 37
[2,4,1,5,3] => 38
[2,4,3,1,5] => 39
[2,4,3,5,1] => 40
[2,4,5,1,3] => 41
[2,4,5,3,1] => 42
[2,5,1,3,4] => 43
[2,5,1,4,3] => 44
[2,5,3,1,4] => 45
[2,5,3,4,1] => 46
[2,5,4,1,3] => 47
[2,5,4,3,1] => 48
[3,1,2,4,5] => 49
[3,1,2,5,4] => 50
[3,1,4,2,5] => 51
[3,1,4,5,2] => 52
[3,1,5,2,4] => 53
[3,1,5,4,2] => 54
[3,2,1,4,5] => 55
[3,2,1,5,4] => 56
[3,2,4,1,5] => 57
[3,2,4,5,1] => 58
[3,2,5,1,4] => 59
[3,2,5,4,1] => 60
[3,4,1,2,5] => 61
[3,4,1,5,2] => 62
[3,4,2,1,5] => 63
[3,4,2,5,1] => 64
[3,4,5,1,2] => 65
[3,4,5,2,1] => 66
[3,5,1,2,4] => 67
[3,5,1,4,2] => 68
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Description
The rank of the permutation.
This is its position among all permutations of the same size ordered lexicographically.
This can be computed using the Lehmer code of a permutation:
rank(σ)=1+n−1∑i=1L(σ)i(n−i)!,
where L(σ)i is the i-th entry of the Lehmer code of σ.
This is its position among all permutations of the same size ordered lexicographically.
This can be computed using the Lehmer code of a permutation:
rank(σ)=1+n−1∑i=1L(σ)i(n−i)!,
where L(σ)i is the i-th entry of the Lehmer code of σ.
Code
def statistic(x):
return x.rank()+1
Created
Oct 01, 2011 at 20:56 by Chris Berg
Updated
Jun 28, 2022 at 16:25 by Nadia Lafreniere
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