Processing math: 100%

Identifier
Values
[.,.] => [1] => 1
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 1
[.,[.,[.,.]]] => [3,2,1] => 1
[.,[[.,.],.]] => [2,3,1] => 1
[[.,.],[.,.]] => [1,3,2] => 1
[[.,[.,.]],.] => [2,1,3] => 1
[[[.,.],.],.] => [1,2,3] => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => 1
[.,[[.,.],[.,.]]] => [2,4,3,1] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => 1
[[.,.],[.,[.,.]]] => [1,4,3,2] => 1
[[.,.],[[.,.],.]] => [1,3,4,2] => 1
[[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[[[.,.],.],[.,.]] => [1,2,4,3] => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => 1
[[[.,.],[.,.]],.] => [1,3,2,4] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => 1
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 1
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 1
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 1
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 1
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 1
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 1
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 1
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 1
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 1
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 1
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 1
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 1
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 1
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 1
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 1
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 1
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 1
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 1
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 1
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 1
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 1
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 1
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 1
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 1
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 1
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 1
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 1
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 1
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 1
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 1
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 1
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 1
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 1
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 1
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 1
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 1
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 1
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 1
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 1
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 1
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 1
>>> Load all 347 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 1
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 1
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 1
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 1
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 1
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 1
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 1
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 1
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 1
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 1
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 1
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 1
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 1
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 1
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 1
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 1
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 1
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 1
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 1
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 1
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 1
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 1
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 1
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 1
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 1
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 1
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 1
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 1
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 1
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 1
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 1
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 1
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 1
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 1
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 1
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 1
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 1
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 1
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 1
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 1
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 1
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 1
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 1
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 1
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 1
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 1
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 1
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 1
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 1
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 1
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 1
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 1
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 1
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 1
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 1
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 1
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 1
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 1
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 1
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 1
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 1
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 1
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 1
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 1
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 1
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 1
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 1
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 1
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 1
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 1
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 1
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 1
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 1
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 1
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 1
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 1
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 1
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 1
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 1
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 1
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 1
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 1
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 1
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 1
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 1
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 1
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 1
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 1
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 1
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 1
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 1
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 1
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 1
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 1
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 1
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 1
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 1
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 1
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 1
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 1
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 1
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 1
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 1
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 1
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 1
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 1
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 1
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 1
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 1
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 1
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 1
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 1
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 1
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 1
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 1
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 1
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 1
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 1
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 1
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 1
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 1
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 1
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 1
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 1
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 1
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 1
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 1
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 1
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 1
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 1
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 1
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 1
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 1
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 1
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 1
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 1
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 1
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 1
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 1
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 1
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 1
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 1
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 1
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 1
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 1
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 1
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 1
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 1
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 1
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 1
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 1
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 1
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 1
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 1
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 1
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 1
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 1
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 1
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 1
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 1
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 1
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 1
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 1
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 1
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 1
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 1
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 1
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 1
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 1
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 1
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 1
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 1
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 1
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 1
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 1
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 1
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 1
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 1
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 1
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 1
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 1
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 1
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 1
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 1
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 1
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 1
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 1
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 1
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 1
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 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
Description
The evaluation at 1 of the Kazhdan-Lusztig polynomial with parameters given by the identity and the permutation.
These are multiplicities of Verma modules.
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.