Identifier
Values
{{1}} => [1] => [1] => [.,.] => 0
{{1,2}} => [2,1] => [2,1] => [[.,.],.] => 1
{{1},{2}} => [1,2] => [1,2] => [.,[.,.]] => 0
{{1,2,3}} => [2,3,1] => [3,1,2] => [[.,[.,.]],.] => 2
{{1,2},{3}} => [2,1,3] => [2,1,3] => [[.,.],[.,.]] => 1
{{1,3},{2}} => [3,2,1] => [2,3,1] => [[.,.],[.,.]] => 1
{{1},{2,3}} => [1,3,2] => [1,3,2] => [.,[[.,.],.]] => 0
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 0
{{1,2,3,4}} => [2,3,4,1] => [4,1,2,3] => [[.,[.,[.,.]]],.] => 3
{{1,2,3},{4}} => [2,3,1,4] => [3,1,2,4] => [[.,[.,.]],[.,.]] => 2
{{1,2,4},{3}} => [2,4,3,1] => [3,4,1,2] => [[.,[.,.]],[.,.]] => 2
{{1,2},{3,4}} => [2,1,4,3] => [2,1,4,3] => [[.,.],[[.,.],.]] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [[.,.],[.,[.,.]]] => 1
{{1,3,4},{2}} => [3,2,4,1] => [2,4,1,3] => [[.,.],[[.,.],.]] => 1
{{1,3},{2,4}} => [3,4,1,2] => [3,1,4,2] => [[.,[.,.]],[.,.]] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [2,3,1,4] => [[.,.],[.,[.,.]]] => 1
{{1,4},{2,3}} => [4,3,2,1] => [3,2,4,1] => [[[.,.],.],[.,.]] => 2
{{1},{2,3,4}} => [1,3,4,2] => [1,4,2,3] => [.,[[.,[.,.]],.]] => 0
{{1},{2,3},{4}} => [1,3,2,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 0
{{1,4},{2},{3}} => [4,2,3,1] => [2,3,4,1] => [[.,.],[.,[.,.]]] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [1,3,4,2] => [.,[[.,.],[.,.]]] => 0
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => 4
{{1,2,3,4},{5}} => [2,3,4,1,5] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => 3
{{1,2,3,5},{4}} => [2,3,5,4,1] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => 3
{{1,2,3},{4,5}} => [2,3,1,5,4] => [3,1,2,5,4] => [[.,[.,.]],[[.,.],.]] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => 2
{{1,2,4,5},{3}} => [2,4,3,5,1] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => 2
{{1,2,4},{3,5}} => [2,4,5,1,3] => [4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]] => 3
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => 2
{{1,2,5},{3,4}} => [2,5,4,3,1] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => 3
{{1,2},{3,4,5}} => [2,1,4,5,3] => [2,1,5,3,4] => [[.,.],[[.,[.,.]],.]] => 1
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => 1
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]] => 2
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => 1
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => 1
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => [4,1,3,5,2] => [[.,[[.,.],.]],[.,.]] => 3
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => 3
{{1,3},{2,4,5}} => [3,4,1,5,2] => [3,1,5,2,4] => [[.,[.,.]],[[.,.],.]] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [2,4,5,1,3] => [[.,.],[[.,.],[.,.]]] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => 1
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => [3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]] => 3
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => 2
{{1,5},{2,3,4}} => [5,3,4,2,1] => [4,2,3,5,1] => [[[.,.],[.,.]],[.,.]] => 3
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 0
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 0
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 0
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [2,3,5,1,4] => [[.,.],[.,[[.,.],.]]] => 1
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]] => 2
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [2,4,1,5,3] => [[.,.],[[.,.],[.,.]]] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => 1
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => 2
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => 0
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]] => 0
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 0
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => 0
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 0
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 0
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => 5
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [4,1,2,3,6,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [5,1,2,3,6,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => 4
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [3,1,2,6,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 2
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [3,1,2,5,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [3,1,2,5,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [3,1,2,4,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 2
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [5,1,2,4,6,3] => [[.,[.,[[.,.],.]]],[.,.]] => 4
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [5,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => 4
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [4,1,2,6,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [4,1,2,5,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [4,1,2,5,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [3,4,1,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [4,3,6,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => 3
>>> Load all 278 entries. <<<
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [5,1,2,6,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => 3
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [5,3,4,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => 4
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [2,1,6,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => 1
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [2,1,5,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [4,3,5,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => 3
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [2,1,5,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [4,5,1,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [3,5,1,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [3,4,5,1,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [4,5,3,6,1,2] => [[[.,[.,.]],.],[.,[.,.]]] => 3
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [2,1,4,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [3,5,4,6,1,2] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => 1
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [2,1,3,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 1
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [3,4,5,6,1,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => 1
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [5,1,3,4,6,2] => [[.,[[.,.],[.,.]]],[.,.]] => 4
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [5,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => 4
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [4,1,3,6,2,5] => [[.,[[.,.],.]],[[.,.],.]] => 3
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [4,1,3,5,2,6] => [[.,[[.,.],.]],[.,[.,.]]] => 3
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [4,1,3,5,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => 3
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [2,4,1,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [4,2,6,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => 3
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [5,1,3,6,2,4] => [[.,[[.,.],[.,.]]],[.,.]] => 4
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [5,2,4,6,1,3] => [[[.,.],[[.,.],.]],[.,.]] => 4
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [3,1,6,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => 2
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [3,1,5,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [4,2,5,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [3,1,5,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [3,1,4,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [4,5,1,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => 3
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [2,5,1,3,6,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [2,4,5,1,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [4,5,2,6,1,3] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [3,1,4,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [3,1,4,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [2,5,4,6,1,3] => [[.,.],[[[.,.],.],[.,.]]] => 1
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [3,1,5,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [2,3,1,6,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 1
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [2,4,5,6,1,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [3,1,4,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [3,2,6,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [5,1,4,6,2,3] => [[.,[[.,[.,.]],.]],[.,.]] => 4
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [3,2,5,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => 2
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [5,2,3,6,1,4] => [[[.,.],[.,[.,.]]],[.,.]] => 4
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [4,1,6,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => 3
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [4,1,5,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [3,2,5,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => 2
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [4,1,5,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => 2
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => 2
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [4,2,3,6,1,5] => [[[.,.],[.,.]],[[.,.],.]] => 3
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [5,1,6,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => 4
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [4,2,3,5,1,6] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [5,2,3,4,6,1] => [[[.,.],[.,[.,.]]],[.,.]] => 4
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 0
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [4,2,3,5,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,4,2,3,6,5] => [.,[[.,[.,.]],[[.,.],.]]] => 0
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [3,2,4,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => 2
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [4,5,1,6,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [[[.,.],.],[[.,.],[.,.]]] => 2
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 2
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [4,5,2,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 0
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,5,2,3,6,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,5,4,6,2,3] => [.,[[[.,[.,.]],.],[.,.]]] => 0
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,3,2,6,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 0
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 0
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 0
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 0
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [2,3,6,1,4,5] => [[.,.],[.,[[.,[.,.]],.]]] => 1
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [3,5,1,4,6,2] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [2,5,1,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => 1
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [2,3,5,1,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [3,5,2,6,1,4] => [[[.,.],.],[[.,.],[.,.]]] => 2
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [3,4,1,6,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => 2
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [[.,[.,[.,.]]],[.,[.,.]]] => 3
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [3,4,1,5,2,6] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [2,5,3,6,1,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [4,1,5,3,6,2] => [[.,[[.,.],.]],[.,[.,.]]] => 3
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [2,4,1,6,3,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [2,4,1,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [2,3,5,6,1,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [3,4,1,5,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [2,4,1,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [3,4,2,6,1,5] => [[[.,.],.],[.,[[.,.],.]]] => 2
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [3,5,1,6,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => 2
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [4,2,5,1,6,3] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => 2
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [3,5,2,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => 2
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 0
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,5,2,4,6,3] => [.,[[.,[[.,.],.]],[.,.]]] => 0
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 0
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [4,2,5,3,6,1] => [[[.,.],[.,.]],[.,[.,.]]] => 3
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,5,3,6,2,4] => [.,[[[.,.],[.,.]],[.,.]]] => 0
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,4,2,6,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 0
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,4,2,5,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => 0
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,4,2,5,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 0
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [2,4,3,6,1,5] => [[.,.],[[.,.],[[.,.],.]]] => 1
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [4,3,5,1,6,2] => [[[.,[.,.]],.],[.,[.,.]]] => 3
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [2,5,1,6,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => 3
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,4,3,6,2,5] => [.,[[[.,.],.],[[.,.],.]]] => 0
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,5,2,6,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 0
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => 0
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [2,5,3,4,6,1] => [[.,.],[[.,[.,.]],[.,.]]] => 1
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,5,3,4,6,2] => [.,[[[.,.],[.,.]],[.,.]]] => 0
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 0
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 0
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 0
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 0
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => 0
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [2,3,4,6,1,5] => [[.,.],[.,[.,[[.,.],.]]]] => 1
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [3,4,5,1,6,2] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [2,4,5,1,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [2,3,5,1,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => 2
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => 0
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,4,5,2,6,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 0
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,3,5,2,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => 0
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => 1
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => 0
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => 0
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,5,3,6,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 0
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => 1
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => 0
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => 0
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 0
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => 1
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 0
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 0
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 0
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 0
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Description
The size of the left subtree of a binary tree.
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.