Identifier
Values
[1] => [1] => 1
[1,2] => [2,1] => 1
[2,1] => [1,2] => 2
[1,2,3] => [3,2,1] => 1
[1,3,2] => [3,1,2] => 2
[2,1,3] => [2,3,1] => 2
[2,3,1] => [2,1,3] => 4
[3,1,2] => [1,3,2] => 4
[3,2,1] => [1,2,3] => 6
[1,2,3,4] => [4,3,2,1] => 1
[1,2,4,3] => [4,3,1,2] => 2
[1,3,2,4] => [4,2,3,1] => 2
[1,3,4,2] => [4,2,1,3] => 4
[1,4,2,3] => [4,1,3,2] => 4
[1,4,3,2] => [4,1,2,3] => 6
[2,1,3,4] => [3,4,2,1] => 2
[2,1,4,3] => [3,4,1,2] => 4
[2,3,1,4] => [3,2,4,1] => 4
[2,3,4,1] => [3,2,1,4] => 8
[2,4,1,3] => [3,1,4,2] => 8
[2,4,3,1] => [3,1,2,4] => 12
[3,1,2,4] => [2,4,3,1] => 4
[3,1,4,2] => [2,4,1,3] => 8
[3,2,1,4] => [2,3,4,1] => 6
[3,2,4,1] => [2,3,1,4] => 12
[3,4,1,2] => [2,1,4,3] => 14
[3,4,2,1] => [2,1,3,4] => 18
[4,1,2,3] => [1,4,3,2] => 8
[4,1,3,2] => [1,4,2,3] => 12
[4,2,1,3] => [1,3,4,2] => 12
[4,2,3,1] => [1,3,2,4] => 20
[4,3,1,2] => [1,2,4,3] => 18
[4,3,2,1] => [1,2,3,4] => 24
[1,2,3,4,5] => [5,4,3,2,1] => 1
[1,2,3,5,4] => [5,4,3,1,2] => 2
[1,2,4,3,5] => [5,4,2,3,1] => 2
[1,2,4,5,3] => [5,4,2,1,3] => 4
[1,2,5,3,4] => [5,4,1,3,2] => 4
[1,2,5,4,3] => [5,4,1,2,3] => 6
[1,3,2,4,5] => [5,3,4,2,1] => 2
[1,3,2,5,4] => [5,3,4,1,2] => 4
[1,3,4,2,5] => [5,3,2,4,1] => 4
[1,3,4,5,2] => [5,3,2,1,4] => 8
[1,3,5,2,4] => [5,3,1,4,2] => 8
[1,3,5,4,2] => [5,3,1,2,4] => 12
[1,4,2,3,5] => [5,2,4,3,1] => 4
[1,4,2,5,3] => [5,2,4,1,3] => 8
[1,4,3,2,5] => [5,2,3,4,1] => 6
[1,4,3,5,2] => [5,2,3,1,4] => 12
[1,4,5,2,3] => [5,2,1,4,3] => 14
[1,4,5,3,2] => [5,2,1,3,4] => 18
[1,5,2,3,4] => [5,1,4,3,2] => 8
[1,5,2,4,3] => [5,1,4,2,3] => 12
[1,5,3,2,4] => [5,1,3,4,2] => 12
[1,5,3,4,2] => [5,1,3,2,4] => 20
[1,5,4,2,3] => [5,1,2,4,3] => 18
[1,5,4,3,2] => [5,1,2,3,4] => 24
[2,1,3,4,5] => [4,5,3,2,1] => 2
[2,1,3,5,4] => [4,5,3,1,2] => 4
[2,1,4,3,5] => [4,5,2,3,1] => 4
[2,1,4,5,3] => [4,5,2,1,3] => 8
[2,1,5,3,4] => [4,5,1,3,2] => 8
[2,1,5,4,3] => [4,5,1,2,3] => 12
[2,3,1,4,5] => [4,3,5,2,1] => 4
[2,3,1,5,4] => [4,3,5,1,2] => 8
[2,3,4,1,5] => [4,3,2,5,1] => 8
[2,3,4,5,1] => [4,3,2,1,5] => 16
[2,3,5,1,4] => [4,3,1,5,2] => 16
[2,3,5,4,1] => [4,3,1,2,5] => 24
[2,4,1,3,5] => [4,2,5,3,1] => 8
[2,4,1,5,3] => [4,2,5,1,3] => 16
[2,4,3,1,5] => [4,2,3,5,1] => 12
[2,4,3,5,1] => [4,2,3,1,5] => 24
[2,4,5,1,3] => [4,2,1,5,3] => 28
[2,4,5,3,1] => [4,2,1,3,5] => 36
[2,5,1,3,4] => [4,1,5,3,2] => 16
[2,5,1,4,3] => [4,1,5,2,3] => 24
[2,5,3,1,4] => [4,1,3,5,2] => 24
[2,5,3,4,1] => [4,1,3,2,5] => 40
[2,5,4,1,3] => [4,1,2,5,3] => 36
[2,5,4,3,1] => [4,1,2,3,5] => 48
[3,1,2,4,5] => [3,5,4,2,1] => 4
[3,1,2,5,4] => [3,5,4,1,2] => 8
[3,1,4,2,5] => [3,5,2,4,1] => 8
[3,1,4,5,2] => [3,5,2,1,4] => 16
[3,1,5,2,4] => [3,5,1,4,2] => 16
[3,1,5,4,2] => [3,5,1,2,4] => 24
[3,2,1,4,5] => [3,4,5,2,1] => 6
[3,2,1,5,4] => [3,4,5,1,2] => 12
[3,2,4,1,5] => [3,4,2,5,1] => 12
[3,2,4,5,1] => [3,4,2,1,5] => 24
[3,2,5,1,4] => [3,4,1,5,2] => 24
[3,2,5,4,1] => [3,4,1,2,5] => 36
[3,4,1,2,5] => [3,2,5,4,1] => 14
[3,4,1,5,2] => [3,2,5,1,4] => 28
[3,4,2,1,5] => [3,2,4,5,1] => 18
[3,4,2,5,1] => [3,2,4,1,5] => 36
[3,4,5,1,2] => [3,2,1,5,4] => 46
[3,4,5,2,1] => [3,2,1,4,5] => 54
[3,5,1,2,4] => [3,1,5,4,2] => 28
[3,5,1,4,2] => [3,1,5,2,4] => 44
>>> Load all 153 entries. <<<
[3,5,2,1,4] => [3,1,4,5,2] => 36
[3,5,2,4,1] => [3,1,4,2,5] => 60
[3,5,4,1,2] => [3,1,2,5,4] => 60
[3,5,4,2,1] => [3,1,2,4,5] => 72
[4,1,2,3,5] => [2,5,4,3,1] => 8
[4,1,2,5,3] => [2,5,4,1,3] => 16
[4,1,3,2,5] => [2,5,3,4,1] => 12
[4,1,3,5,2] => [2,5,3,1,4] => 24
[4,1,5,2,3] => [2,5,1,4,3] => 28
[4,1,5,3,2] => [2,5,1,3,4] => 36
[4,2,1,3,5] => [2,4,5,3,1] => 12
[4,2,1,5,3] => [2,4,5,1,3] => 24
[4,2,3,1,5] => [2,4,3,5,1] => 20
[4,2,3,5,1] => [2,4,3,1,5] => 40
[4,2,5,1,3] => [2,4,1,5,3] => 44
[4,2,5,3,1] => [2,4,1,3,5] => 60
[4,3,1,2,5] => [2,3,5,4,1] => 18
[4,3,1,5,2] => [2,3,5,1,4] => 36
[4,3,2,1,5] => [2,3,4,5,1] => 24
[4,3,2,5,1] => [2,3,4,1,5] => 48
[4,3,5,1,2] => [2,3,1,5,4] => 60
[4,3,5,2,1] => [2,3,1,4,5] => 72
[4,5,1,2,3] => [2,1,5,4,3] => 46
[4,5,1,3,2] => [2,1,5,3,4] => 60
[4,5,2,1,3] => [2,1,4,5,3] => 60
[4,5,2,3,1] => [2,1,4,3,5] => 88
[4,5,3,1,2] => [2,1,3,5,4] => 78
[4,5,3,2,1] => [2,1,3,4,5] => 96
[5,1,2,3,4] => [1,5,4,3,2] => 16
[5,1,2,4,3] => [1,5,4,2,3] => 24
[5,1,3,2,4] => [1,5,3,4,2] => 24
[5,1,3,4,2] => [1,5,3,2,4] => 40
[5,1,4,2,3] => [1,5,2,4,3] => 36
[5,1,4,3,2] => [1,5,2,3,4] => 48
[5,2,1,3,4] => [1,4,5,3,2] => 24
[5,2,1,4,3] => [1,4,5,2,3] => 36
[5,2,3,1,4] => [1,4,3,5,2] => 40
[5,2,3,4,1] => [1,4,3,2,5] => 68
[5,2,4,1,3] => [1,4,2,5,3] => 60
[5,2,4,3,1] => [1,4,2,3,5] => 84
[5,3,1,2,4] => [1,3,5,4,2] => 36
[5,3,1,4,2] => [1,3,5,2,4] => 60
[5,3,2,1,4] => [1,3,4,5,2] => 48
[5,3,2,4,1] => [1,3,4,2,5] => 84
[5,3,4,1,2] => [1,3,2,5,4] => 88
[5,3,4,2,1] => [1,3,2,4,5] => 108
[5,4,1,2,3] => [1,2,5,4,3] => 54
[5,4,1,3,2] => [1,2,5,3,4] => 72
[5,4,2,1,3] => [1,2,4,5,3] => 72
[5,4,2,3,1] => [1,2,4,3,5] => 108
[5,4,3,1,2] => [1,2,3,5,4] => 96
[5,4,3,2,1] => [1,2,3,4,5] => 120
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Description
The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$