Identifier
Values
[.,.] => [1] => [1] => [.,.] => 0
[.,[.,.]] => [2,1] => [1,2] => [.,[.,.]] => 1
[[.,.],.] => [1,2] => [1,2] => [.,[.,.]] => 1
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => [.,[.,[.,.]]] => 3
[.,[[.,.],.]] => [2,3,1] => [1,2,3] => [.,[.,[.,.]]] => 3
[[.,.],[.,.]] => [3,1,2] => [1,2,3] => [.,[.,[.,.]]] => 3
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => [.,[[.,.],.]] => 2
[[[.,.],.],.] => [1,2,3] => [1,2,3] => [.,[.,[.,.]]] => 3
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[.,[.,[[.,.],.]]] => [3,4,2,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[.,[[.,.],[.,.]]] => [4,2,3,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[.,[[.,[.,.]],.]] => [3,2,4,1] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 5
[.,[[[.,.],.],.]] => [2,3,4,1] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[[.,.],[.,[.,.]]] => [4,3,1,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[[.,.],[[.,.],.]] => [3,4,1,2] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[[.,[.,.]],[.,.]] => [4,2,1,3] => [1,3,2,4] => [.,[[.,.],[.,.]]] => 4
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[[.,[.,[.,.]]],.] => [3,2,1,4] => [1,4,2,3] => [.,[[.,[.,.]],.]] => 4
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,4,2,3] => [.,[[.,[.,.]],.]] => 4
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,2,4,3] => [.,[.,[[.,.],.]]] => 5
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,4,2] => [.,[[.,.],[.,.]]] => 4
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => 6
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 9
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 8
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 8
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 8
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 9
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 8
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 9
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 7
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => 7
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 6
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]] => 6
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => 8
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => 7
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 7
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 7
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 7
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [1,5,2,4,3] => [.,[[.,[[.,.],.]],.]] => 6
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]] => 7
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 8
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]] => 8
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [1,3,5,2,4] => [.,[[.,.],[[.,.],.]]] => 6
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => 9
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 6
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]] => 6
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => 8
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => 7
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => 10
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]] => 11
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => 11
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
>>> Load all 201 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => 10
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [1,4,2,3,5,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [1,5,2,4,3,6] => [.,[[.,[[.,.],.]],[.,.]]] => 8
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [1,5,2,3,4,6] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [1,2,5,3,4,6] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [1,3,5,2,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => 9
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [1,4,5,2,3,6] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => 10
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [1,6,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],.]] => 9
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]] => 9
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [1,6,2,5,3,4] => [.,[[.,[[.,[.,.]],.]],.]] => 9
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [1,6,2,3,5,4] => [.,[[.,[.,[[.,.],.]]],.]] => 10
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [1,6,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],.]] => 9
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => [.,[[.,[.,[.,[.,.]]]],.]] => 11
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [1,2,6,3,5,4] => [.,[.,[[.,[[.,.],.]],.]]] => 11
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [1,2,6,3,4,5] => [.,[.,[[.,[.,[.,.]]],.]]] => 12
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 9
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [1,3,6,2,4,5] => [.,[[.,.],[[.,[.,.]],.]]] => 9
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [1,2,3,6,4,5] => [.,[.,[.,[[.,[.,.]],.]]]] => 13
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 8
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [1,4,6,2,3,5] => [.,[[.,[.,.]],[[.,.],.]]] => 8
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [1,2,4,6,3,5] => [.,[.,[[.,.],[[.,.],.]]]] => 11
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [1,3,4,6,2,5] => [.,[[.,.],[.,[[.,.],.]]]] => 10
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => 14
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [1,5,6,2,4,3] => [.,[[.,[[.,.],.]],[.,.]]] => 8
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [1,5,6,2,3,4] => [.,[[.,[.,[.,.]]],[.,.]]] => 9
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [1,2,5,6,3,4] => [.,[.,[[.,[.,.]],[.,.]]]] => 11
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [1,3,5,6,2,4] => [.,[[.,.],[[.,.],[.,.]]]] => 9
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => 13
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [1,4,5,6,2,3] => [.,[[.,[.,.]],[.,[.,.]]]] => 9
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => 12
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => 11
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => 15
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [1,6,2,4,3,5,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [1,6,2,4,5,3,7] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [1,6,7,2,4,3,5] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [1,6,7,2,4,5,3] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => 11
[[.,[[.,[[.,[[.,.],.]],.]],.]],.] => [4,5,3,6,2,7,1,8] => [1,8,2,7,3,6,4,5] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => 16
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Description
The sum of the sizes of the right subtrees of a binary tree.
This statistic corresponds to St000012The area of a Dyck path. under the Tamari Dyck path-binary tree bijection, and to St000018The number of inversions of a permutation. of the $312$-avoiding permutation corresponding to the binary tree.
It is also the sum of all heights $j$ of the coordinates $(i,j)$ of the Dyck path corresponding to the binary tree.
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
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.