Identifier
Values
[[]] => [.,.] => [1] => [1] => 1
[[],[]] => [[.,.],.] => [1,2] => [1,2] => 2
[[[]]] => [.,[.,.]] => [2,1] => [2,1] => 1
[[],[],[]] => [[[.,.],.],.] => [1,2,3] => [1,2,3] => 3
[[],[[]]] => [[.,.],[.,.]] => [1,3,2] => [3,1,2] => 2
[[[]],[]] => [[.,[.,.]],.] => [2,1,3] => [2,1,3] => 2
[[[],[]]] => [.,[[.,.],.]] => [2,3,1] => [2,3,1] => 2
[[[[]]]] => [.,[.,[.,.]]] => [3,2,1] => [3,2,1] => 1
[[],[],[],[]] => [[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 4
[[],[],[[]]] => [[[.,.],.],[.,.]] => [1,2,4,3] => [4,1,2,3] => 3
[[],[[]],[]] => [[[.,.],[.,.]],.] => [1,3,2,4] => [3,1,2,4] => 3
[[],[[],[]]] => [[.,.],[[.,.],.]] => [1,3,4,2] => [3,4,1,2] => 2
[[],[[[]]]] => [[.,.],[.,[.,.]]] => [1,4,3,2] => [4,3,1,2] => 2
[[[]],[],[]] => [[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => 3
[[[]],[[]]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => [2,4,1,3] => 2
[[[],[]],[]] => [[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1,4] => 2
[[[[]]],[]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1,4] => 2
[[[],[],[]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,4,1] => 3
[[[],[[]]]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => [4,2,3,1] => 2
[[[[]],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,4,1] => 2
[[[[],[]]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => [3,4,2,1] => 2
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,2,1] => 1
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 5
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [5,1,2,3,4] => 4
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [4,1,2,3,5] => 4
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [4,5,1,2,3] => 3
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [5,4,1,2,3] => 3
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [3,1,2,4,5] => 4
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [3,5,1,2,4] => 3
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [3,4,1,2,5] => 3
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [4,3,1,2,5] => 3
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [3,4,5,1,2] => 3
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [5,3,4,1,2] => 2
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [4,3,5,1,2] => 2
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [4,5,3,1,2] => 2
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [5,4,3,1,2] => 2
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => 4
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,5,1,3,4] => 3
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,4,1,3,5] => 3
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,4,5,1,3] => 3
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [5,2,4,1,3] => 2
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4,5] => 3
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4,5] => 3
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [2,3,5,1,4] => 3
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [3,2,5,1,4] => 2
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1,5] => 3
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [4,2,3,1,5] => 2
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1,5] => 2
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1,5] => 2
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1,5] => 2
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,5,1] => 4
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [5,2,3,4,1] => 3
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [4,2,3,5,1] => 3
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [4,5,2,3,1] => 2
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [5,4,2,3,1] => 2
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,5,1] => 3
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [3,5,2,4,1] => 2
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,5,1] => 2
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,5,1] => 2
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,5,2,1] => 3
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [5,3,4,2,1] => 2
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,5,2,1] => 2
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,5,3,2,1] => 2
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,3,2,1] => 1
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 6
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [6,1,2,3,4,5] => 5
[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [5,1,2,3,4,6] => 5
[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [5,6,1,2,3,4] => 4
[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [6,5,1,2,3,4] => 4
[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [4,1,2,3,5,6] => 5
[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [4,6,1,2,3,5] => 4
[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [4,5,1,2,3,6] => 4
[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [5,4,1,2,3,6] => 4
[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [4,5,6,1,2,3] => 3
[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [6,4,5,1,2,3] => 3
[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [5,4,6,1,2,3] => 3
[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [5,6,4,1,2,3] => 3
[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [6,5,4,1,2,3] => 3
[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [3,1,2,4,5,6] => 5
[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [3,6,1,2,4,5] => 4
[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [3,5,1,2,4,6] => 4
[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [3,5,6,1,2,4] => 3
[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [6,3,5,1,2,4] => 3
[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [3,4,1,2,5,6] => 4
[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [4,3,1,2,5,6] => 4
[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [3,4,6,1,2,5] => 3
[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [4,3,6,1,2,5] => 3
[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [3,4,5,1,2,6] => 3
[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [5,3,4,1,2,6] => 3
[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [4,3,5,1,2,6] => 3
[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [4,5,3,1,2,6] => 3
[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [5,4,3,1,2,6] => 3
[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [3,4,5,6,1,2] => 4
[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [6,3,4,5,1,2] => 3
[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [5,3,4,6,1,2] => 3
[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [5,6,3,4,1,2] => 2
[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [6,5,3,4,1,2] => 2
[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [4,3,5,6,1,2] => 3
[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [4,6,3,5,1,2] => 2
[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [4,5,3,6,1,2] => 2
[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [5,4,3,6,1,2] => 2
>>> Load all 284 entries. <<<
[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [4,5,6,3,1,2] => 3
[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [6,4,5,3,1,2] => 2
[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [5,4,6,3,1,2] => 2
[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [5,6,4,3,1,2] => 2
[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [6,5,4,3,1,2] => 2
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 5
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,6,1,3,4,5] => 4
[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,5,1,3,4,6] => 4
[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,5,6,1,3,4] => 3
[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [6,2,5,1,3,4] => 3
[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,4,1,3,5,6] => 4
[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,4,6,1,3,5] => 3
[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,4,5,1,3,6] => 3
[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [5,2,4,1,3,6] => 3
[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,4,5,6,1,3] => 4
[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [6,2,4,5,1,3] => 3
[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [5,2,4,6,1,3] => 3
[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [5,6,2,4,1,3] => 2
[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [6,5,2,4,1,3] => 2
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5,6] => 4
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 4
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [2,3,6,1,4,5] => 3
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [3,2,6,1,4,5] => 3
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [2,3,5,1,4,6] => 3
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [3,2,5,1,4,6] => 3
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [2,3,5,6,1,4] => 4
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [6,2,3,5,1,4] => 3
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [3,2,5,6,1,4] => 3
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [3,6,2,5,1,4] => 2
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5,6] => 3
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [4,2,3,1,5,6] => 3
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5,6] => 3
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5,6] => 3
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 3
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [2,3,4,6,1,5] => 4
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [4,2,3,6,1,5] => 3
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [3,2,4,6,1,5] => 3
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [3,4,2,6,1,5] => 2
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [4,3,2,6,1,5] => 2
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1,6] => 4
[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [5,2,3,4,1,6] => 3
[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [4,2,3,5,1,6] => 3
[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [4,5,2,3,1,6] => 2
[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [5,4,2,3,1,6] => 2
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1,6] => 3
[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [3,5,2,4,1,6] => 2
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1,6] => 2
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1,6] => 2
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1,6] => 3
[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [5,3,4,2,1,6] => 2
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1,6] => 2
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1,6] => 2
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 2
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,6,1] => 5
[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [6,2,3,4,5,1] => 4
[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [5,2,3,4,6,1] => 4
[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [5,6,2,3,4,1] => 3
[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [6,5,2,3,4,1] => 3
[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [4,2,3,5,6,1] => 4
[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [4,6,2,3,5,1] => 3
[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [4,5,2,3,6,1] => 3
[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [5,4,2,3,6,1] => 3
[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [4,5,6,2,3,1] => 3
[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [6,4,5,2,3,1] => 2
[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [5,4,6,2,3,1] => 2
[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [5,6,4,2,3,1] => 2
[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [6,5,4,2,3,1] => 2
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,6,1] => 4
[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [3,6,2,4,5,1] => 3
[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [3,5,2,4,6,1] => 3
[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [3,5,6,2,4,1] => 3
[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [6,3,5,2,4,1] => 2
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,6,1] => 3
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,6,1] => 3
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [3,4,6,2,5,1] => 3
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [4,3,6,2,5,1] => 2
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,6,1] => 3
[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [5,3,4,2,6,1] => 2
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,6,1] => 2
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,6,1] => 2
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,6,1] => 2
[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,6,2,1] => 4
[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [6,3,4,5,2,1] => 3
[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [5,3,4,6,2,1] => 3
[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [5,6,3,4,2,1] => 2
[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [6,5,3,4,2,1] => 2
[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,6,2,1] => 3
[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [4,6,3,5,2,1] => 2
[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,6,2,1] => 2
[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,6,2,1] => 2
[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,6,3,2,1] => 3
[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [6,4,5,3,2,1] => 2
[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,6,3,2,1] => 2
[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,6,4,3,2,1] => 2
[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 1
[[],[],[],[],[],[],[]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 7
[[],[],[],[],[],[[]]] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => 6
[[],[],[],[],[[]],[]] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [6,1,2,3,4,5,7] => 6
[[],[],[],[],[[[]]]] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => 5
[[],[],[],[[]],[],[]] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [5,1,2,3,4,6,7] => 6
[[],[],[],[[[]]],[]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => 5
[[],[],[],[[[[]]]]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => 4
[[],[],[[]],[],[],[]] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [4,1,2,3,5,6,7] => 6
[[],[],[[[]]],[],[]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => 5
[[],[],[[[[]]]],[]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [6,5,4,1,2,3,7] => 4
[[],[],[[[[[]]]]]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [7,6,5,4,1,2,3] => 3
[[],[[]],[],[],[],[]] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [3,1,2,4,5,6,7] => 6
[[],[[[]]],[],[],[]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [4,3,1,2,5,6,7] => 5
[[],[[[[]]]],[],[]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [1,5,4,3,2,6,7] => [5,4,3,1,2,6,7] => 4
[[],[[[[[]]]]],[]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7] => [6,5,4,3,1,2,7] => 3
[[[]],[],[],[],[],[]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 6
[[[],[]],[],[],[],[]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6,7] => 5
[[[[]]],[],[],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 5
[[[],[],[]],[],[],[]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6,7] => 4
[[[],[[]]],[],[],[]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [2,4,3,1,5,6,7] => [4,2,3,1,5,6,7] => 4
[[[[]],[]],[],[],[]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6,7] => 4
[[[[],[]]],[],[],[]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6,7] => 4
[[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 4
[[[],[],[],[]],[],[]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6,7] => 4
[[[],[],[[]]],[],[]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [2,3,5,4,1,6,7] => [5,2,3,4,1,6,7] => 3
[[[],[[]],[]],[],[]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7] => [4,2,3,5,1,6,7] => 3
[[[],[[[]]]],[],[]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [2,5,4,3,1,6,7] => [5,4,2,3,1,6,7] => 3
[[[[]],[],[]],[],[]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6,7] => 3
[[[[],[]],[]],[],[]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6,7] => 3
[[[[[]]],[]],[],[]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6,7] => 3
[[[[],[],[]]],[],[]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6,7] => 3
[[[[],[[]]]],[],[]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [3,5,4,2,1,6,7] => [5,3,4,2,1,6,7] => 3
[[[[[]],[]]],[],[]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6,7] => 3
[[[[[],[]]]],[],[]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6,7] => 3
[[[[[[]]]]],[],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 3
[[[],[],[],[],[]],[]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1,7] => 5
[[[],[],[],[[]]],[]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [2,3,4,6,5,1,7] => [6,2,3,4,5,1,7] => 4
[[[],[],[[]],[]],[]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [2,3,5,4,6,1,7] => [5,2,3,4,6,1,7] => 4
[[[],[],[[[]]]],[]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [6,5,2,3,4,1,7] => 3
[[[],[[]],[],[]],[]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [2,4,3,5,6,1,7] => [4,2,3,5,6,1,7] => 4
[[[],[[[]]],[]],[]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [2,5,4,3,6,1,7] => [5,4,2,3,6,1,7] => 3
[[[[]],[],[],[]],[]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1,7] => 4
[[[[],[]],[],[]],[]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1,7] => 3
[[[[[]]],[],[]],[]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1,7] => 3
[[[[],[],[]],[]],[]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1,7] => 3
[[[[],[],[],[]]],[]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1,7] => 4
[[[[],[],[[]]]],[]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [3,4,6,5,2,1,7] => [6,3,4,5,2,1,7] => 3
[[[[],[[]],[]]],[]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [3,5,4,6,2,1,7] => [5,3,4,6,2,1,7] => 3
[[[[[]],[],[]]],[]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1,7] => 3
[[[[[],[],[]]]],[]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => 3
[[[],[],[],[],[],[]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,7,1] => 6
[[[],[],[],[],[[]]]] => [.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [7,2,3,4,5,6,1] => 5
[[[],[],[],[[]],[]]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1] => [6,2,3,4,5,7,1] => 5
[[[],[],[],[[[]]]]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [7,6,2,3,4,5,1] => 4
[[[],[],[[]],[],[]]] => [.,[[[[[.,.],.],[.,.]],.],.]] => [2,3,5,4,6,7,1] => [5,2,3,4,6,7,1] => 5
[[[],[],[[[]]],[]]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1] => [6,5,2,3,4,7,1] => 4
[[[],[],[[[[]]]]]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [7,6,5,2,3,4,1] => 3
[[[],[[]],[],[],[]]] => [.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [4,2,3,5,6,7,1] => 5
[[[],[[[]]],[],[]]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [2,5,4,3,6,7,1] => [5,4,2,3,6,7,1] => 4
[[[],[[[[]]]],[]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1] => [6,5,4,2,3,7,1] => 3
[[[[]],[],[],[],[]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,7,1] => 5
[[[[],[]],[],[],[]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,7,1] => 4
[[[[[]]],[],[],[]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,7,1] => 4
[[[[],[],[]],[],[]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,7,1] => 3
[[[[],[[]]],[],[]]] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [3,5,4,2,6,7,1] => [5,3,4,2,6,7,1] => 3
[[[[[]],[]],[],[]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,7,1] => 3
[[[[[],[]]],[],[]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,7,1] => 3
[[[[[[]]]],[],[]]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,7,1] => 3
[[[[],[],[],[]],[]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,7,1] => 4
[[[[],[],[[]]],[]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [3,4,6,5,2,7,1] => [6,3,4,5,2,7,1] => 3
[[[[],[[]],[]],[]]] => [.,[[.,[[[.,.],[.,.]],.]],.]] => [3,5,4,6,2,7,1] => [5,3,4,6,2,7,1] => 3
[[[[[]],[],[]],[]]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,7,1] => 3
[[[[[],[],[]]],[]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,7,1] => 3
[[[[],[],[],[],[]]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,7,2,1] => 5
[[[[],[],[],[[]]]]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [3,4,5,7,6,2,1] => [7,3,4,5,6,2,1] => 4
[[[[],[],[[]],[]]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1] => [6,3,4,5,7,2,1] => 4
[[[[],[],[[[]]]]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [3,4,7,6,5,2,1] => [7,6,3,4,5,2,1] => 3
[[[[],[[]],[],[]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => [3,5,4,6,7,2,1] => [5,3,4,6,7,2,1] => 4
[[[[],[[[]]],[]]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1] => [6,5,3,4,7,2,1] => 3
[[[[[]],[],[],[]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,7,2,1] => 4
[[[[[],[]],[],[]]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,7,2,1] => 3
[[[[[[]]],[],[]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,7,2,1] => 3
[[[[[],[],[]],[]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,7,2,1] => 3
[[[[[],[],[],[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,7,3,2,1] => 4
[[[[[],[],[[]]]]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [4,5,7,6,3,2,1] => [7,4,5,6,3,2,1] => 3
[[[[[],[[]],[]]]]] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1] => [6,4,5,7,3,2,1] => 3
[[[[[[]],[],[]]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,7,3,2,1] => 3
[[[[[[],[],[]]]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,7,4,3,2,1] => 3
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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Description
The height of the tree associated to a permutation.
A permutation can be mapped to a rooted tree with vertices $\{0,1,2,\ldots,n\}$ and root $0$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1].
The statistic is given by the height of this tree.
See also St000325The width of the tree associated to a permutation. for the width of this tree.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
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.