Identifier
Values
[1,0,1,0] => [1,2] => [1,2] => [.,[.,.]] => 1
[1,1,0,0] => [2,1] => [1,2] => [.,[.,.]] => 1
[1,0,1,0,1,0] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 2
[1,0,1,1,0,0] => [1,3,2] => [1,2,3] => [.,[.,[.,.]]] => 2
[1,1,0,0,1,0] => [2,1,3] => [1,2,3] => [.,[.,[.,.]]] => 2
[1,1,0,1,0,0] => [2,3,1] => [1,2,3] => [.,[.,[.,.]]] => 2
[1,1,1,0,0,0] => [3,2,1] => [1,3,2] => [.,[[.,.],.]] => 1
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 2
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 3
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 2
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [1,3,4,2] => [.,[[.,[.,.]],.]] => 2
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 2
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [1,4,2,3] => [.,[[.,.],[.,.]]] => 2
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 3
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 3
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 3
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 4
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 3
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [1,2,4,5,3] => [.,[.,[[.,[.,.]],.]]] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [1,2,5,3,4] => [.,[.,[[.,.],[.,.]]]] => 3
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 3
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 3
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [1,3,4,5,2] => [.,[[.,[.,[.,.]]],.]] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 3
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [1,3,5,2,4] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [1,3,4,2,5] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 3
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 3
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [1,4,2,3,5] => [.,[[.,.],[.,[.,.]]]] => 3
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [1,4,2,5,3] => [.,[[.,.],[[.,.],.]]] => 2
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [1,5,2,4,3] => [.,[[.,.],[[.,.],.]]] => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 4
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
>>> Load all 195 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 5
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 4
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,[.,.]],.]]]] => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,.],[.,.]]]]] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [1,2,4,5,6,3] => [.,[.,[[.,[.,[.,.]]],.]]] => 4
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [1,2,4,6,3,5] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [1,2,4,5,3,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [1,2,5,3,4,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [1,2,5,3,6,4] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [1,2,6,3,5,4] => [.,[.,[[.,.],[[.,.],.]]]] => 3
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [1,3,4,5,2,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [1,3,4,5,6,2] => [.,[[.,[.,[.,[.,.]]]],.]] => 4
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [1,3,5,4,6,2] => [.,[[.,[[.,.],[.,.]]],.]] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [1,3,5,6,2,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [1,3,5,2,4,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [1,3,6,2,4,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [1,3,4,2,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [1,3,4,6,2,5] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [1,3,6,2,5,4] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [1,3,5,2,6,4] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [1,4,5,6,2,3] => [.,[[.,[.,[.,.]]],[.,.]]] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [1,4,2,3,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [1,4,2,5,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [1,4,2,5,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [1,4,6,2,5,3] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [1,4,3,6,2,5] => [.,[[[.,.],[.,.]],[.,.]]] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [1,4,3,5,2,6] => [.,[[[.,.],[.,.]],[.,.]]] => 3
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [1,5,6,2,4,3] => [.,[[.,[.,.]],[[.,.],.]]] => 3
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [1,5,2,4,6,3] => [.,[[.,.],[[.,[.,.]],.]]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [1,5,2,4,3,6] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [1,5,2,6,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 3
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [.,[[.,.],[[.,.],[.,.]]]] => 3
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Description
The number of left oriented leafs of a binary tree except the first one.
In other other words, this is the sum of canopee vector of the tree.
The canopee of a non empty binary tree T with n internal nodes is the list l of 0 and 1 of length n-1 obtained by going along the leaves of T from left to right except the two extremal ones, writing 0 if the leaf is a right leaf and 1 if the leaf is a left leaf.
This is also the number of nodes having a right child. Indeed each of said right children will give exactly one left oriented leaf.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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.).
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.