Identifier
Values
[.,.] => [1] => 0
[.,[.,.]] => [2,1] => 1
[[.,.],.] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => 3
[.,[[.,.],.]] => [2,3,1] => 2
[[.,.],[.,.]] => [1,3,2] => 1
[[.,[.,.]],.] => [2,1,3] => 1
[[[.,.],.],.] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => 6
[.,[.,[[.,.],.]]] => [3,4,2,1] => 5
[.,[[.,.],[.,.]]] => [2,4,3,1] => 4
[.,[[.,[.,.]],.]] => [3,2,4,1] => 4
[.,[[[.,.],.],.]] => [2,3,4,1] => 3
[[.,.],[.,[.,.]]] => [1,4,3,2] => 3
[[.,.],[[.,.],.]] => [1,3,4,2] => 2
[[.,[.,.]],[.,.]] => [2,1,4,3] => 2
[[[.,.],.],[.,.]] => [1,2,4,3] => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => 2
[[[.,.],[.,.]],.] => [1,3,2,4] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 10
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 9
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 8
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 8
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 7
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 7
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 6
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 6
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 5
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 7
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 6
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 5
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 5
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 4
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 6
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 5
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 4
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 4
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 3
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 4
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 3
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 3
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 2
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 4
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 3
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 2
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 2
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 6
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 5
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 4
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 4
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 3
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 3
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 2
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 2
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 3
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 2
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 15
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 14
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 13
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 13
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 12
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 12
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 11
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 11
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 10
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 12
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 11
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 10
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 10
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 9
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 11
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 10
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 9
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 9
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 8
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 9
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 8
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 8
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 7
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 9
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 8
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 7
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 7
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 6
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 11
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 10
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 9
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 9
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 8
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 8
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 7
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 7
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 6
>>> Load all 389 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 8
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 7
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 6
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 6
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 5
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 10
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 9
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 8
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 8
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 7
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 7
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 6
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 6
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 5
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 7
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 6
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 5
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 5
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 4
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 7
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 6
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 5
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 5
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 4
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 6
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 5
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 4
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 4
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 6
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 5
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 5
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 4
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 4
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 4
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 3
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 3
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 7
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 6
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 5
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 5
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 4
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 4
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 3
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 3
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 2
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 4
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 3
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 2
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 2
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 10
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 9
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 8
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 8
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 7
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 7
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 6
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 6
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 5
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 7
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 6
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 5
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 5
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 4
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 6
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 5
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 4
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 4
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 3
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 4
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 3
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 3
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 4
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 3
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 2
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 2
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 6
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 5
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 4
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 4
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 3
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 3
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 2
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 2
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 3
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 2
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 21
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 10
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 10
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 9
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 9
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 8
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 7
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 6
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 15
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 14
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 13
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 13
[[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 12
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 12
[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 11
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 11
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 12
[[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 11
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 11
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 11
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 11
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 11
[[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 5
[[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 4
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 15
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 14
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 13
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 13
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 12
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 12
[[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 11
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 11
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 12
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 11
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 11
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 11
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 5
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 10
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 4
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 6
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 3
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 3
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 2
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 28
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 26
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 24
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 24
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 22
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 20
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 16
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 20
[.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 12
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 12
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 22
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 20
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 18
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 16
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 14
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 12
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 12
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 10
[.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 10
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 10
[.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 9
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 8
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 7
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 21
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 20
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 19
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 19
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 18
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 18
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 18
[[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 12
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 13
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 13
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 9
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 16
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 10
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 8
[[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 12
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 13
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 9
[[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 4
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 12
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 10
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 8
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 8
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 8
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 8
[[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 6
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 8
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 6
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 6
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 13
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 9
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 6
[[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 4
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 16
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 10
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 8
[[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 6
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 8
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 6
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 6
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 8
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 6
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 6
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 4
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 2
[[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 21
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 20
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 19
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 19
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 18
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 18
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 18
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 13
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 13
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 9
[[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 6
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 6
[[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 4
[[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 2
[[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 2
[[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 1
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 15
[[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 5
[[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 2
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 10
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 4
[[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 2
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 6
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 3
[[[[[[[.,.],[.,.]],.],.],.],.],.] => [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] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1] => 36
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1] => 8
[[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9] => 0
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1] => 45
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1] => 9
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10] => 0
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9] => 28
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10] => 36
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9] => 5
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7,10,9,12,11] => 6
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,9,8] => 1
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,10,9] => 1
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1] => 9
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,7,8,9,11,10] => 1
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1] => 10
[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1] => 10
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1] => 10
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [1,9,8,7,6,5,4,3,2] => 28
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => [7,8,6,5,4,3,2,1,9] => 27
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [1,8,9,7,6,5,4,3,2] => 27
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [1,10,9,8,7,6,5,4,3,2] => 36
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11] => 45
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => [8,9,7,6,5,4,3,2,1,10] => 35
[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => [7,6,8,5,4,3,2,1,9] => 26
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [1,8,7,9,6,5,4,3,2] => 26
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [1,9,10,8,7,6,5,4,3,2] => 35
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [1,11,10,9,8,7,6,5,4,3,2] => 45
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [2,1,10,9,8,7,6,5,4,3] => 29
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => [4,3,2,1,10,9,8,7,6,5] => 21
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => [6,5,4,3,2,1,10,9,8,7] => 21
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => [8,7,6,5,4,3,2,1,10,9] => 29
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9] => 21
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9] => 15
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9] => 10
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9] => 6
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9] => 3
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9] => 1
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10] => 28
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10] => 21
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10] => 15
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10] => 10
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10] => 6
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10] => 3
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10] => 1
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10,11] => 1
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,1,9] => 7
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => [2,3,4,5,6,7,1,8,9] => 6
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => [2,3,4,5,6,7,8,9,1,10] => 8
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Description
The number of inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
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.