Identifier
Values
[1,0] => [1] => 1
[1,0,1,0] => [1,2] => 1
[1,1,0,0] => [2,1] => 2
[1,0,1,0,1,0] => [1,2,3] => 1
[1,0,1,1,0,0] => [1,3,2] => 2
[1,1,0,0,1,0] => [2,1,3] => 2
[1,1,0,1,0,0] => [2,3,1] => 4
[1,1,1,0,0,0] => [3,2,1] => 6
[1,0,1,0,1,0,1,0] => [1,2,3,4] => 1
[1,0,1,0,1,1,0,0] => [1,2,4,3] => 2
[1,0,1,1,0,0,1,0] => [1,3,2,4] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => 4
[1,0,1,1,1,0,0,0] => [1,4,3,2] => 6
[1,1,0,0,1,0,1,0] => [2,1,3,4] => 2
[1,1,0,0,1,1,0,0] => [2,1,4,3] => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => 4
[1,1,0,1,0,1,0,0] => [2,3,4,1] => 8
[1,1,0,1,1,0,0,0] => [2,4,3,1] => 12
[1,1,1,0,0,0,1,0] => [3,2,1,4] => 6
[1,1,1,0,0,1,0,0] => [3,2,4,1] => 12
[1,1,1,0,1,0,0,0] => [3,4,2,1] => 18
[1,1,1,1,0,0,0,0] => [4,3,2,1] => 24
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 6
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 8
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 12
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 6
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 12
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => 18
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 24
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 4
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 4
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 8
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 12
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 8
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 8
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 16
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 24
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 12
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 24
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => 36
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 48
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 6
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 12
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 12
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 24
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 36
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => 18
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => 36
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => 54
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 72
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 24
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 48
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 72
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 96
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 120
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 4
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 8
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 12
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 12
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => 18
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 24
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 8
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 12
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 8
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 8
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 16
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 24
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 12
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 24
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => 36
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 48
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 12
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 12
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 24
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 36
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => 18
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => 36
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => 54
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 72
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 24
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 48
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 72
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 96
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 120
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 4
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 4
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 8
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 12
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 4
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 8
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 8
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 16
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 24
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 12
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 24
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => 36
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 48
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 4
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 8
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 16
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 24
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 8
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 16
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 16
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 32
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 48
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 24
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 48
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => 72
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 96
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 12
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 24
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 24
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 48
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 72
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => 36
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => 72
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => 108
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 144
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 48
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 96
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 144
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 192
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 240
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 12
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 12
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 24
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 36
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 12
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 24
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 24
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 48
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 72
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 36
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 72
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 108
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 144
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => 18
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => 36
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => 36
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => 72
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 108
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => 54
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => 108
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => 162
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 216
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 72
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 144
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 216
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 288
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 360
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 24
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 48
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 48
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 96
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 144
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 72
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 144
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 216
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 288
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 96
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 192
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 288
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 384
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 480
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 120
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 240
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 360
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 480
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 600
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 720
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searching the database for statistics with the same generating function
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Description
The number of elements less than or equal to the given element in Bruhat order.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).