Identifier
Values
[1,0] => [.,.] => [1] => [1] => 1
[1,0,1,0] => [.,[.,.]] => [2,1] => [2,1] => 1
[1,1,0,0] => [[.,.],.] => [1,2] => [1,2] => 2
[1,0,1,0,1,0] => [.,[.,[.,.]]] => [3,2,1] => [3,2,1] => 1
[1,0,1,1,0,0] => [.,[[.,.],.]] => [2,3,1] => [3,1,2] => 2
[1,1,0,0,1,0] => [[.,.],[.,.]] => [1,3,2] => [2,3,1] => 2
[1,1,0,1,0,0] => [[.,[.,.]],.] => [2,1,3] => [2,1,3] => 2
[1,1,1,0,0,0] => [[[.,.],.],.] => [1,2,3] => [1,2,3] => 3
[1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => 1
[1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [4,3,1,2] => 2
[1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => [2,4,3,1] => [4,2,3,1] => 2
[1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => [3,2,4,1] => [4,2,1,3] => 2
[1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1] => [4,1,2,3] => 3
[1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => [1,4,3,2] => [3,4,2,1] => 2
[1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => [1,3,4,2] => [2,4,1,3] => 2
[1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => [2,1,4,3] => [3,2,4,1] => 2
[1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => 2
[1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],.] => [2,3,1,4] => [3,1,2,4] => 3
[1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => [1,2,4,3] => [2,3,4,1] => 3
[1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],.] => [1,3,2,4] => [2,3,1,4] => 3
[1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => 3
[1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 4
[1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => 1
[1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [5,4,3,1,2] => 2
[1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,4,2,3,1] => 2
[1,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [5,4,2,1,3] => 2
[1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [5,4,1,2,3] => 3
[1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,3,4,2,1] => 2
[1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [5,2,4,1,3] => 2
[1,0,1,1,0,1,0,0,1,0] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [5,3,2,4,1] => 2
[1,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,3,2,1,4] => 2
[1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,3,1,2,4] => 3
[1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,2,3,4,1] => 3
[1,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,2,3,1,4] => 3
[1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,2,1,3,4] => 3
[1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,1,2,3,4] => 4
[1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [4,5,3,2,1] => 2
[1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [3,5,4,1,2] => 2
[1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [3,5,2,4,1] => 2
[1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [3,5,2,1,4] => 2
[1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [2,5,1,3,4] => 3
[1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [4,3,5,2,1] => 2
[1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [3,2,5,1,4] => 2
[1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [4,3,2,5,1] => 2
[1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => 2
[1,1,0,1,0,1,1,0,0,0] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [4,3,1,2,5] => 3
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [4,2,3,5,1] => 3
[1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,2,3,1,5] => 3
[1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,2,1,3,5] => 3
[1,1,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,1,2,3,5] => 4
[1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [3,4,5,2,1] => 3
[1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [2,3,5,1,4] => 3
[1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [3,4,2,5,1] => 3
[1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [3,4,2,1,5] => 3
[1,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [2,4,1,3,5] => 3
[1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [3,2,4,5,1] => 3
[1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [3,2,4,1,5] => 3
[1,1,1,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => 3
[1,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,1,2,4,5] => 4
[1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [2,3,4,5,1] => 4
[1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [2,3,4,1,5] => 4
[1,1,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [2,3,1,4,5] => 4
[1,1,1,1,0,1,0,0,0,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => 4
[1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,5,4,2,3,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [6,5,2,4,1,3] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [6,5,3,2,4,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,5,2,3,4,1] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [6,5,2,3,1,4] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,4,5,3,2,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [6,3,5,4,1,2] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,3,5,2,4,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [6,3,5,2,1,4] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [6,2,5,1,3,4] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,4,3,5,2,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [6,3,2,5,1,4] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [6,4,3,2,5,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [6,4,2,3,5,1] => 3
[1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,4,2,3,1,5] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => 3
[1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,3,4,5,2,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [6,2,3,5,1,4] => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [6,3,4,2,5,1] => 3
[1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,3,4,2,1,5] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,2,4,1,3,5] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [6,3,2,4,5,1] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,3,2,4,1,5] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => 3
[1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => 4
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,2,3,4,1,5] => 4
[1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,2,3,1,4,5] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [5,6,4,3,2,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [4,6,5,3,1,2] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [4,6,5,2,3,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [4,6,5,2,1,3] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [3,6,5,1,2,4] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [4,6,3,5,2,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [3,6,2,5,1,4] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [4,6,3,2,5,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [4,6,3,2,1,5] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [3,6,4,1,2,5] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [3,6,2,4,5,1] => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [3,6,2,4,1,5] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [3,6,2,1,4,5] => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [2,6,1,3,4,5] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [5,4,6,3,2,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [4,3,6,5,1,2] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [4,3,6,2,5,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [4,3,6,2,1,5] => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [3,2,6,1,4,5] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [5,4,3,6,2,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [4,3,2,6,1,5] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [5,4,3,2,6,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 2
[1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [5,4,2,3,6,1] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,4,2,3,1,6] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [5,3,4,6,2,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [4,2,3,6,1,5] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [5,3,4,2,6,1] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,3,4,2,1,6] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [5,2,4,1,3,6] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [5,3,2,4,6,1] => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [5,3,2,4,1,6] => 3
[1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [5,2,3,4,6,1] => 4
[1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,2,3,1,4,6] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [4,5,6,3,2,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [3,4,6,5,1,2] => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [3,4,6,2,5,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [3,4,6,2,1,5] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [2,3,6,1,4,5] => 4
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [4,5,3,6,2,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [3,4,2,6,1,5] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [4,5,3,2,6,1] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [4,5,3,2,1,6] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [3,5,4,1,2,6] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [3,5,2,4,6,1] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [3,5,2,4,1,6] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [3,5,2,1,4,6] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [2,5,1,3,4,6] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [4,3,5,6,2,1] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [3,2,4,6,1,5] => 3
[1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [4,3,5,2,6,1] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [4,3,5,2,1,6] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [3,2,5,1,4,6] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [4,3,2,5,6,1] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [4,3,2,5,1,6] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 4
[1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [4,2,3,5,6,1] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [4,2,3,5,1,6] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [3,4,5,6,2,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [2,3,4,6,1,5] => 4
[1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [3,4,5,2,6,1] => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [3,4,5,2,1,6] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [2,3,5,1,4,6] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [3,4,2,5,6,1] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [3,4,2,5,1,6] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [3,4,2,1,5,6] => 4
[1,1,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [2,4,1,3,5,6] => 4
[1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [3,2,4,5,6,1] => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [3,2,4,5,1,6] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [3,2,4,1,5,6] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 4
[1,1,1,1,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [2,3,4,5,6,1] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [2,3,4,5,1,6] => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [2,3,4,1,5,6] => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [2,3,1,4,5,6] => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 6
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Description
The length of the longest increasing subsequence of the permutation.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.