Identifier
Values
{{1}} => [1] => [1] => 1
{{1,2}} => [2,1] => [1,2] => 1
{{1},{2}} => [1,2] => [2,1] => 1
{{1,2,3}} => [2,3,1] => [1,3,2] => 2
{{1,2},{3}} => [2,1,3] => [3,1,2] => 1
{{1,3},{2}} => [3,2,1] => [1,2,3] => 1
{{1},{2,3}} => [1,3,2] => [2,3,1] => 1
{{1},{2},{3}} => [1,2,3] => [3,2,1] => 1
{{1,2,3,4}} => [2,3,4,1] => [1,4,3,2] => 5
{{1,2,3},{4}} => [2,3,1,4] => [4,1,3,2] => 2
{{1,2,4},{3}} => [2,4,3,1] => [1,3,4,2] => 3
{{1,2},{3,4}} => [2,1,4,3] => [3,4,1,2] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [4,3,1,2] => 1
{{1,3,4},{2}} => [3,2,4,1] => [1,4,2,3] => 3
{{1,3},{2,4}} => [3,4,1,2] => [2,1,4,3] => 3
{{1,3},{2},{4}} => [3,2,1,4] => [4,1,2,3] => 1
{{1,4},{2,3}} => [4,3,2,1] => [1,2,3,4] => 1
{{1},{2,3,4}} => [1,3,4,2] => [2,4,3,1] => 2
{{1},{2,3},{4}} => [1,3,2,4] => [4,2,3,1] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [1,3,2,4] => 2
{{1},{2,4},{3}} => [1,4,3,2] => [2,3,4,1] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [3,4,2,1] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [4,3,2,1] => 1
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,5,4,3,2] => 14
{{1,2,3,4},{5}} => [2,3,4,1,5] => [5,1,4,3,2] => 5
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,4,5,3,2] => 9
{{1,2,3},{4,5}} => [2,3,1,5,4] => [4,5,1,3,2] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [5,4,1,3,2] => 2
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,5,3,4,2] => 10
{{1,2,4},{3,5}} => [2,4,5,1,3] => [3,1,5,4,2] => 8
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [5,1,3,4,2] => 3
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,3,4,5,2] => 4
{{1,2},{3,4,5}} => [2,1,4,5,3] => [3,5,4,1,2] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [5,3,4,1,2] => 1
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,4,3,5,2] => 7
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [3,4,5,1,2] => 1
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [4,5,3,1,2] => 1
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [5,4,3,1,2] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,5,4,2,3] => 9
{{1,3,4},{2,5}} => [3,5,4,1,2] => [2,1,4,5,3] => 6
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [5,1,4,2,3] => 3
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,2,5,4,3] => 14
{{1,3},{2,4,5}} => [3,4,1,5,2] => [2,5,1,4,3] => 8
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [5,2,1,4,3] => 3
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,4,5,2,3] => 6
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [2,4,1,5,3] => 5
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [4,5,1,2,3] => 1
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [5,4,1,2,3] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,5,2,3,4] => 4
{{1,4},{2,3,5}} => [4,3,5,1,2] => [2,1,5,3,4] => 6
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [5,1,2,3,4] => 1
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,2,4,3,5] => 3
{{1},{2,3,4,5}} => [1,3,4,5,2] => [2,5,4,3,1] => 5
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [5,2,4,3,1] => 2
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,4,2,3,5] => 3
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [2,4,5,3,1] => 3
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [4,5,2,3,1] => 1
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [5,4,2,3,1] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,5,3,2,4] => 7
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [2,1,3,5,4] => 4
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [3,1,5,2,4] => 5
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [5,1,3,2,4] => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,2,3,4,5] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [2,5,3,4,1] => 3
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [3,2,5,4,1] => 3
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [5,2,3,4,1] => 1
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,3,4,2,5] => 3
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [2,3,4,5,1] => 1
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [3,5,4,2,1] => 2
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [5,3,4,2,1] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,4,3,2,5] => 5
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [2,4,3,5,1] => 2
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [3,4,5,2,1] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [4,5,3,2,1] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [5,4,3,2,1] => 1
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,6,5,4,3,2] => 42
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [6,1,5,4,3,2] => 14
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,5,6,4,3,2] => 28
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [5,6,1,4,3,2] => 5
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [6,5,1,4,3,2] => 5
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [1,6,4,5,3,2] => 32
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [4,1,6,5,3,2] => 23
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [6,1,4,5,3,2] => 9
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [1,4,5,6,3,2] => 14
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [4,6,5,1,3,2] => 4
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [6,4,5,1,3,2] => 2
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [1,5,4,6,3,2] => 23
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [4,5,6,1,3,2] => 2
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [5,6,4,1,3,2] => 2
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [6,5,4,1,3,2] => 2
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [1,6,5,3,4,2] => 32
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [3,1,5,6,4,2] => 20
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [6,1,5,3,4,2] => 10
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [1,3,6,5,4,2] => 58
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [3,6,1,5,4,2] => 21
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [6,3,1,5,4,2] => 8
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [1,5,6,3,4,2] => 22
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [3,5,1,6,4,2] => 13
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [5,6,1,3,4,2] => 3
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [6,5,1,3,4,2] => 3
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [1,6,3,4,5,2] => 17
>>> Load all 301 entries. <<<
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [3,1,6,4,5,2] => 21
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [6,1,3,4,5,2] => 4
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [1,3,5,4,6,2] => 14
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [3,6,5,4,1,2] => 5
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [6,3,5,4,1,2] => 2
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [1,5,3,4,6,2] => 13
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [3,5,6,4,1,2] => 3
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [5,6,3,4,1,2] => 1
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [6,5,3,4,1,2] => 1
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [1,6,4,3,5,2] => 26
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [3,1,4,6,5,2] => 15
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [4,1,6,3,5,2] => 17
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [6,1,4,3,5,2] => 7
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [1,3,4,5,6,2] => 5
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [3,6,4,5,1,2] => 3
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [4,3,6,5,1,2] => 3
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [6,3,4,5,1,2] => 1
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [1,4,5,3,6,2] => 12
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [3,4,5,6,1,2] => 1
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [4,6,5,3,1,2] => 2
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [6,4,5,3,1,2] => 1
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [1,5,4,3,6,2] => 19
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [3,5,4,6,1,2] => 2
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [4,5,6,3,1,2] => 1
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [5,6,4,3,1,2] => 1
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [6,5,4,3,1,2] => 1
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,6,5,4,2,3] => 28
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [2,1,5,4,6,3] => 25
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [6,1,5,4,2,3] => 9
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [1,2,6,4,5,3] => 46
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [2,6,1,4,5,3] => 21
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [6,2,1,4,5,3] => 6
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [1,5,6,4,2,3] => 19
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [2,5,1,4,6,3] => 15
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [5,6,1,4,2,3] => 3
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [6,5,1,4,2,3] => 3
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [1,6,2,5,4,3] => 58
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [2,1,6,5,4,3] => 84
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [6,1,2,5,4,3] => 14
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [1,2,5,6,4,3] => 40
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [2,6,5,1,4,3] => 23
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [6,2,5,1,4,3] => 8
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [1,5,2,6,4,3] => 44
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [2,5,6,1,4,3] => 15
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [5,6,2,1,4,3] => 3
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [6,5,2,1,4,3] => 3
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [1,6,4,5,2,3] => 22
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [2,1,4,5,6,3] => 10
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [4,1,6,5,2,3] => 15
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [6,1,4,5,2,3] => 6
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [1,2,4,6,5,3] => 35
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [2,6,4,1,5,3] => 17
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [4,2,6,1,5,3] => 13
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [6,2,4,1,5,3] => 5
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [1,4,5,6,2,3] => 10
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [2,4,5,1,6,3] => 7
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [4,6,5,1,2,3] => 2
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [6,4,5,1,2,3] => 1
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [1,5,4,6,2,3] => 16
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [2,5,4,1,6,3] => 12
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [4,5,6,1,2,3] => 1
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [5,6,4,1,2,3] => 1
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [6,5,4,1,2,3] => 1
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [1,6,5,2,3,4] => 14
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [2,1,5,6,3,4] => 20
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [6,1,5,2,3,4] => 4
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [1,2,6,5,3,4] => 40
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [2,6,1,5,3,4] => 20
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [6,2,1,5,3,4] => 6
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [1,5,6,2,3,4] => 10
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [2,5,1,6,3,4] => 14
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [5,6,1,2,3,4] => 1
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [6,5,1,2,3,4] => 1
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [1,6,2,4,3,5] => 14
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [2,1,6,4,3,5] => 25
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [6,1,2,4,3,5] => 3
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,2,5,4,3,6] => 14
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [2,6,5,4,3,1] => 14
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [6,2,5,4,3,1] => 5
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,5,2,4,3,6] => 11
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [2,5,6,4,3,1] => 9
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [5,6,2,4,3,1] => 2
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [6,5,2,4,3,1] => 2
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [1,6,4,2,3,5] => 12
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [2,1,4,6,3,5] => 20
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [4,1,6,2,3,5] => 7
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [6,1,4,2,3,5] => 3
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [1,2,4,5,3,6] => 6
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [2,6,4,5,3,1] => 10
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [4,2,6,5,3,1] => 8
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [6,2,4,5,3,1] => 3
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,4,5,2,3,6] => 6
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [2,4,5,6,3,1] => 4
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [4,6,5,2,3,1] => 2
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [6,4,5,2,3,1] => 1
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,5,4,2,3,6] => 9
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [2,5,4,6,3,1] => 7
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [4,5,6,2,3,1] => 1
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [5,6,4,2,3,1] => 1
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [6,5,4,2,3,1] => 1
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [1,6,5,3,2,4] => 23
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [2,1,5,3,6,4] => 20
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [3,1,5,6,2,4] => 14
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [6,1,5,3,2,4] => 7
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [1,2,6,3,5,4] => 35
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [2,6,1,3,5,4] => 15
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [3,2,1,6,5,4] => 30
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [6,2,1,3,5,4] => 4
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [1,3,6,5,2,4] => 44
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [2,3,1,5,6,4] => 10
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [3,6,1,5,2,4] => 13
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [6,3,1,5,2,4] => 5
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [1,5,6,3,2,4] => 16
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [2,5,1,3,6,4] => 11
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [3,5,1,6,2,4] => 8
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [5,6,1,3,2,4] => 2
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [6,5,1,3,2,4] => 2
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [1,6,2,3,4,5] => 5
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [2,1,6,3,4,5] => 10
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [3,1,2,6,4,5] => 10
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [6,1,2,3,4,5] => 1
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [1,2,5,3,4,6] => 6
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [2,6,5,3,4,1] => 9
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [3,2,5,6,4,1] => 6
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [6,2,5,3,4,1] => 3
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [1,3,2,5,4,6] => 8
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [2,3,6,5,4,1] => 14
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [3,6,2,5,4,1] => 8
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [6,3,2,5,4,1] => 3
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [1,5,2,3,4,6] => 4
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [2,5,6,3,4,1] => 6
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [3,5,2,6,4,1] => 5
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [5,6,2,3,4,1] => 1
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [6,5,2,3,4,1] => 1
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [1,6,3,4,2,5] => 13
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [2,1,3,4,6,5] => 5
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [3,1,6,4,2,5] => 15
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [6,1,3,4,2,5] => 3
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [1,2,3,4,5,6] => 1
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [2,6,3,4,5,1] => 4
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [3,2,6,4,5,1] => 6
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [6,2,3,4,5,1] => 1
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,3,5,4,2,6] => 11
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [2,3,5,4,6,1] => 3
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [3,6,5,4,2,1] => 5
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [6,3,5,4,2,1] => 2
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,5,3,4,2,6] => 10
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [2,5,3,4,6,1] => 3
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [3,5,6,4,2,1] => 3
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [5,6,3,4,2,1] => 1
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [6,5,3,4,2,1] => 1
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [1,6,4,3,2,5] => 19
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [2,1,4,3,6,5] => 15
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [3,1,4,6,2,5] => 11
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [4,1,6,3,2,5] => 12
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [6,1,4,3,2,5] => 5
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [1,2,4,3,5,6] => 3
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [2,6,4,3,5,1] => 7
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [3,2,4,6,5,1] => 4
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [4,2,6,3,5,1] => 5
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [6,2,4,3,5,1] => 2
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [1,3,4,5,2,6] => 4
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [2,3,4,5,6,1] => 1
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [3,6,4,5,2,1] => 3
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [4,3,6,5,2,1] => 3
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [6,3,4,5,2,1] => 1
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,4,5,3,2,6] => 9
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [2,4,5,3,6,1] => 3
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [3,4,5,6,2,1] => 1
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [4,6,5,3,2,1] => 2
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [6,4,5,3,2,1] => 1
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,5,4,3,2,6] => 14
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [2,5,4,3,6,1] => 5
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [3,5,4,6,2,1] => 2
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [4,5,6,3,2,1] => 1
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [5,6,4,3,2,1] => 1
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [6,5,4,3,2,1] => 1
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [1,7,6,5,4,3,2] => 132
{{1,2,3,4,5,7},{6}} => [2,3,4,5,7,6,1] => [1,6,7,5,4,3,2] => 90
{{1,2,3,4,7},{5,6}} => [2,3,4,7,6,5,1] => [1,5,6,7,4,3,2] => 48
{{1,2,3,4,7},{5},{6}} => [2,3,4,7,5,6,1] => [1,6,5,7,4,3,2] => 76
{{1,2,3,5,6,7},{4}} => [2,3,5,4,6,7,1] => [1,7,6,4,5,3,2] => 107
{{1,2,3,5,7},{4,6}} => [2,3,5,6,7,4,1] => [1,4,7,6,5,3,2] => 211
{{1,2,3,6,7},{4,5}} => [2,3,6,5,4,7,1] => [1,7,4,5,6,3,2] => 62
{{1,2,3,6,7},{4},{5}} => [2,3,6,4,5,7,1] => [1,7,5,4,6,3,2] => 89
{{1,2,3,7},{4},{5,6}} => [2,3,7,4,6,5,1] => [1,5,6,4,7,3,2] => 43
{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [1,6,5,4,7,3,2] => 66
{{1,2,4,6,7},{3,5}} => [2,4,5,6,3,7,1] => [1,7,3,6,5,4,2] => 251
{{1,2,6,7},{3},{4,5}} => [2,6,3,5,4,7,1] => [1,7,4,5,3,6,2] => 54
{{1,2,6,7},{3},{4},{5}} => [2,6,3,4,5,7,1] => [1,7,5,4,3,6,2] => 75
{{1,2},{3,7},{4,6},{5}} => [2,1,7,6,5,4,3] => [3,4,5,6,7,1,2] => 1
{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [1,6,5,4,3,7,2] => 56
{{1,4,7},{2,3},{5,6}} => [4,3,2,7,6,5,1] => [1,5,6,7,2,3,4] => 20
{{1,4},{2,3},{5,7},{6}} => [4,3,2,1,7,6,5] => [5,6,7,1,2,3,4] => 1
{{1,5,7},{2,4},{3},{6}} => [5,4,3,2,7,6,1] => [1,6,7,2,3,4,5] => 15
{{1,5},{2,4,7},{3},{6}} => [5,4,3,7,1,6,2] => [2,6,1,7,3,4,5] => 30
{{1,6,7},{2,5},{3,4}} => [6,5,4,3,2,7,1] => [1,7,2,3,4,5,6] => 6
{{1,6},{2,5,7},{3,4}} => [6,5,4,3,7,1,2] => [2,1,7,3,4,5,6] => 15
{{1,7},{2,6},{3,5},{4}} => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => 1
{{1},{2,7},{3,6},{4,5}} => [1,7,6,5,4,3,2] => [2,3,4,5,6,7,1] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of reduced Kogan faces with the permutation as type.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.