Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000109
(load all 4 compositions to match this statistic)
Mapping
Mp00069: Permutations —complement⟶ Permutations
St000109: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => 1
[1,2] => [2,1] => 2
[2,1] => [1,2] => 1
[1,2,3] => [3,2,1] => 6
[1,3,2] => [3,1,2] => 4
[2,1,3] => [2,3,1] => 4
[2,3,1] => [2,1,3] => 2
[3,1,2] => [1,3,2] => 2
[3,2,1] => [1,2,3] => 1
[1,2,3,4] => [4,3,2,1] => 24
[1,2,4,3] => [4,3,1,2] => 18
[1,3,2,4] => [4,2,3,1] => 20
[1,3,4,2] => [4,2,1,3] => 12
[1,4,2,3] => [4,1,3,2] => 12
[1,4,3,2] => [4,1,2,3] => 8
[2,1,3,4] => [3,4,2,1] => 18
[2,1,4,3] => [3,4,1,2] => 14
[2,3,1,4] => [3,2,4,1] => 12
[2,3,4,1] => [3,2,1,4] => 6
[2,4,1,3] => [3,1,4,2] => 8
[2,4,3,1] => [3,1,2,4] => 4
[3,1,2,4] => [2,4,3,1] => 12
[3,1,4,2] => [2,4,1,3] => 8
[3,2,1,4] => [2,3,4,1] => 8
[3,2,4,1] => [2,3,1,4] => 4
[3,4,1,2] => [2,1,4,3] => 4
[3,4,2,1] => [2,1,3,4] => 2
[4,1,2,3] => [1,4,3,2] => 6
[4,1,3,2] => [1,4,2,3] => 4
[4,2,1,3] => [1,3,4,2] => 4
[4,2,3,1] => [1,3,2,4] => 2
[4,3,1,2] => [1,2,4,3] => 2
[4,3,2,1] => [1,2,3,4] => 1
[1,2,3,4,5] => [5,4,3,2,1] => 120
[1,2,3,5,4] => [5,4,3,1,2] => 96
[1,2,4,3,5] => [5,4,2,3,1] => 108
[1,2,4,5,3] => [5,4,2,1,3] => 72
[1,2,5,3,4] => [5,4,1,3,2] => 72
[1,2,5,4,3] => [5,4,1,2,3] => 54
[1,3,2,4,5] => [5,3,4,2,1] => 108
[1,3,2,5,4] => [5,3,4,1,2] => 88
[1,3,4,2,5] => [5,3,2,4,1] => 84
[1,3,4,5,2] => [5,3,2,1,4] => 48
[1,3,5,2,4] => [5,3,1,4,2] => 60
[1,3,5,4,2] => [5,3,1,2,4] => 36
[1,4,2,3,5] => [5,2,4,3,1] => 84
[1,4,2,5,3] => [5,2,4,1,3] => 60
[1,4,3,2,5] => [5,2,3,4,1] => 68
[1,4,3,5,2] => [5,2,3,1,4] => 40
[1,4,5,2,3] => [5,2,1,4,3] => 36
Description
The number of elements less than or equal to the given element in Bruhat order.
Matching statistic: St000033
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Mapping
St000033: Permutations ⟶ ℤResult quality: 18% ●values known / values provided: 18%●distinct values known / distinct values provided: 33%
Values
[1] => 1
[1,2] => 2
[2,1] => 1
[1,2,3] => 6
[1,3,2] => 4
[2,1,3] => 4
[2,3,1] => 2
[3,1,2] => 2
[3,2,1] => 1
[1,2,3,4] => 24
[1,2,4,3] => 18
[1,3,2,4] => 20
[1,3,4,2] => 12
[1,4,2,3] => 12
[1,4,3,2] => 8
[2,1,3,4] => 18
[2,1,4,3] => 14
[2,3,1,4] => 12
[2,3,4,1] => 6
[2,4,1,3] => 8
[2,4,3,1] => 4
[3,1,2,4] => 12
[3,1,4,2] => 8
[3,2,1,4] => 8
[3,2,4,1] => 4
[3,4,1,2] => 4
[3,4,2,1] => 2
[4,1,2,3] => 6
[4,1,3,2] => 4
[4,2,1,3] => 4
[4,2,3,1] => 2
[4,3,1,2] => 2
[4,3,2,1] => 1
[1,2,3,4,5] => 120
[1,2,3,5,4] => 96
[1,2,4,3,5] => 108
[1,2,4,5,3] => 72
[1,2,5,3,4] => 72
[1,2,5,4,3] => 54
[1,3,2,4,5] => 108
[1,3,2,5,4] => 88
[1,3,4,2,5] => 84
[1,3,4,5,2] => 48
[1,3,5,2,4] => 60
[1,3,5,4,2] => 36
[1,4,2,3,5] => 84
[1,4,2,5,3] => 60
[1,4,3,2,5] => 68
[1,4,3,5,2] => 40
[1,4,5,2,3] => 36
[1,2,3,4,5,6] => ? = 720
[1,2,3,4,6,5] => ? = 600
[1,2,3,5,4,6] => ? = 672
[1,2,3,5,6,4] => ? = 480
[1,2,3,6,4,5] => ? = 480
[1,2,3,6,5,4] => ? = 384
[1,2,4,3,5,6] => ? = 684
[1,2,4,3,6,5] => ? = 576
[1,2,4,5,3,6] => ? = 576
[1,2,4,5,6,3] => ? = 360
[1,2,4,6,3,5] => ? = 432
[1,2,4,6,5,3] => ? = 288
[1,2,5,3,4,6] => ? = 576
[1,2,5,3,6,4] => ? = 432
[1,2,5,4,3,6] => ? = 504
[1,2,5,4,6,3] => ? = 324
[1,2,5,6,3,4] => ? = 288
[1,2,5,6,4,3] => ? = 216
[1,2,6,3,4,5] => ? = 360
[1,2,6,3,5,4] => ? = 288
[1,2,6,4,3,5] => ? = 324
[1,2,6,4,5,3] => ? = 216
[1,2,6,5,3,4] => ? = 216
[1,2,6,5,4,3] => ? = 162
[1,3,2,4,5,6] => ? = 672
[1,3,2,4,6,5] => ? = 564
[1,3,2,5,4,6] => ? = 632
[1,3,2,5,6,4] => ? = 456
[1,3,2,6,4,5] => ? = 456
[1,3,2,6,5,4] => ? = 368
[1,3,4,2,5,6] => ? = 576
[1,3,4,2,6,5] => ? = 492
[1,3,4,5,2,6] => ? = 432
[1,3,4,5,6,2] => ? = 240
[1,3,4,6,2,5] => ? = 336
[1,3,4,6,5,2] => ? = 192
[1,3,5,2,4,6] => ? = 504
[1,3,5,2,6,4] => ? = 384
[1,3,5,4,2,6] => ? = 384
[1,3,5,4,6,2] => ? = 216
[1,3,5,6,2,4] => ? = 240
[1,3,5,6,4,2] => ? = 144
[1,3,6,2,4,5] => ? = 324
[1,3,6,2,5,4] => ? = 264
[1,3,6,4,2,5] => ? = 252
[1,3,6,4,5,2] => ? = 144
[1,3,6,5,2,4] => ? = 180
[1,3,6,5,4,2] => ? = 108
[1,4,2,3,5,6] => ? = 576
[1,4,2,3,6,5] => ? = 492
Description
The number of permutations greater than or equal to the given permutation in (strong) Bruhat order.