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 304 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
[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => 10
[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => 9
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 11
[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => 10
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 9
[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 9
[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => 8
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 9
[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 8
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => 8
[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => 7
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => 8
[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => 7
[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => 7
[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => 6
[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => 8
[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => 8
[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => 7
[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => 7
[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => 6
[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => 7
[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => 6
[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => 6
[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => 5
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 10
[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => 9
[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => 8
[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => 8
[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => 7
[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 7
[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 6
[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 6
[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 5
[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 7
[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => 6
[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 5
[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 5
[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => 4
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 7
[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 6
[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 5
[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 5
[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 6
[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => 5
[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 4
[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 4
[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 3
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 6
[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 5
[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 5
[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 4
[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 3
[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 4
[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 3
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 3
[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 2
[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => 6
[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 5
[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 5
[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => 4
[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 4
[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 3
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 2
[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 4
[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 3
[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 2
[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 1
[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => 8
[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => 7
[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 7
[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 6
[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 6
[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => 5
[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => 6
[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => 5
[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => 5
[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => 4
[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 6
[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => 5
[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 4
[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 4
[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 3
[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 4
[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 3
[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 3
[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 2
[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 4
[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 3
[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 2
[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 1
[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => 5
[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 4
[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 4
[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => 3
[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 3
[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 2
[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 2
[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 1
[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 3
[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 2
[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
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Description
The number of transpositions that are smaller or equal to a permutation in Bruhat order.
A statistic is known to be smooth if and only if this number coincides with the number of inversions. This is also equivalent for a permutation to avoid the two pattern $4231$ and $3412$.
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.