Identifier
Values
[[]] => [.,.] => [1] => 0
[[],[]] => [[.,.],.] => [1,2] => 0
[[[]]] => [.,[.,.]] => [2,1] => 1
[[],[],[]] => [[[.,.],.],.] => [1,2,3] => 0
[[],[[]]] => [[.,.],[.,.]] => [1,3,2] => 1
[[[]],[]] => [[.,[.,.]],.] => [2,1,3] => 1
[[[],[]]] => [.,[[.,.],.]] => [2,3,1] => 1
[[[[]]]] => [.,[.,[.,.]]] => [3,2,1] => 2
[[],[],[],[]] => [[[[.,.],.],.],.] => [1,2,3,4] => 0
[[],[],[[]]] => [[[.,.],.],[.,.]] => [1,2,4,3] => 1
[[],[[]],[]] => [[[.,.],[.,.]],.] => [1,3,2,4] => 1
[[],[[],[]]] => [[.,.],[[.,.],.]] => [1,3,4,2] => 1
[[],[[[]]]] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 2
[[[]],[],[]] => [[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[[]],[[]]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 1
[[[],[]],[]] => [[.,[[.,.],.]],.] => [2,3,1,4] => 1
[[[[]]],[]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 2
[[[],[],[]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => 1
[[[],[[]]]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 2
[[[[]],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 2
[[[[],[]]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 2
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 3
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 1
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 1
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 1
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 2
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 1
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 1
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 1
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 2
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 1
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 2
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 2
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 2
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 3
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 1
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 1
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 1
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 2
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 1
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 2
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 1
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 2
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 1
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 2
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 2
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 2
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 3
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 1
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 2
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 2
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 2
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 3
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 2
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 2
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 2
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 3
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 2
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 3
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 3
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 3
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 4
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 1
[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 1
[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 1
[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 2
[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 1
[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 1
[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 1
[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 2
[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 1
[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 2
[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 2
[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 2
[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 3
[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 1
[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 1
[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 1
[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 1
[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 2
[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 1
[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 2
[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 1
[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 2
[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 1
[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 2
[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 2
[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 2
[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 3
[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 1
[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 2
[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 2
[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 2
[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 3
[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 2
[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 2
[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 2
[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 3
>>> Load all 341 entries. <<<
[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 2
[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 3
[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 3
[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 3
[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 4
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 1
[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 1
[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 1
[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 2
[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 1
[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 1
[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 1
[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 2
[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 1
[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 2
[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 2
[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 2
[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 3
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 1
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 2
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 1
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 2
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 1
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 2
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 1
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 2
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 2
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 2
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 1
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 2
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 2
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 2
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 3
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 1
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 2
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 2
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 2
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 3
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 1
[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 2
[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 2
[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 2
[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 3
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 2
[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 2
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 2
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 3
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 2
[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 3
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 3
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 3
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 4
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 1
[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 2
[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 2
[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 2
[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 3
[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 2
[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 2
[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 2
[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 3
[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 2
[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 3
[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 3
[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 3
[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 4
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 2
[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 2
[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 2
[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 2
[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 3
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 2
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 3
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 2
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 3
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 2
[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 3
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 3
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 3
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 4
[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 2
[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 3
[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 3
[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 3
[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 4
[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 3
[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 3
[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 3
[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 4
[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 3
[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 4
[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 4
[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 4
[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 5
[[],[],[],[],[],[],[]] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
[[],[],[],[],[],[[]]] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 1
[[],[],[],[],[[]],[]] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 1
[[],[[]],[],[],[],[]] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 1
[[],[[],[[[[]]]]]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 4
[[],[[[[[]]]],[]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => 4
[[],[[[],[[],[]]]]] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => 3
[[],[[[],[[[]]]]]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => 4
[[],[[[[]],[[]]]]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => 3
[[],[[[[],[]],[]]]] => [[.,.],[.,[[.,[[.,.],.]],.]]] => [1,5,6,4,7,3,2] => 3
[[],[[[[[]]],[]]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [1,6,5,4,7,3,2] => 4
[[],[[[[],[],[]]]]] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [1,5,6,7,4,3,2] => 3
[[],[[[[],[[]]]]]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => 4
[[],[[[[[]],[]]]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [1,6,5,7,4,3,2] => 4
[[],[[[[[],[]]]]]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => 4
[[],[[[[[[]]]]]]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => 5
[[[]],[],[],[],[],[]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => 1
[[[]],[[[[[]]]]]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => 4
[[[],[]],[],[],[],[]] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => 1
[[[[]]],[],[],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => 2
[[[],[],[]],[],[],[]] => [[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => 1
[[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => 3
[[[],[],[]],[],[[]]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [2,3,4,1,5,7,6] => 1
[[[],[],[],[]],[],[]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => 1
[[[[[[]]]]],[],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => 4
[[[],[],[],[]],[[]]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [2,3,4,5,1,7,6] => 1
[[[[[[]]]]],[[]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => 4
[[[],[],[],[],[]],[]] => [[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => 1
[[[],[[[[]]]]],[]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => 4
[[[[[[]]]],[]],[]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => 4
[[[[],[[],[]]]],[]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [3,5,6,4,2,1,7] => 3
[[[[],[[[]]]]],[]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => 4
[[[[[]],[[]]]],[]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => 3
[[[[[],[]],[]]],[]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => 3
[[[[[[]]],[]]],[]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => 4
[[[[[],[],[]]]],[]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => 3
[[[[[],[[]]]]],[]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => 4
[[[[[[]],[]]]],[]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => 4
[[[[[[],[]]]]],[]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => 4
[[[[[[[]]]]]],[]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => 5
[[[],[],[],[],[],[]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => 1
[[[[]],[],[],[],[]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => 2
[[[[],[]],[],[],[]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => 2
[[[[[]]],[],[],[]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => 3
[[[[],[],[]],[],[]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => 2
[[[[[]],[]],[],[]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => 3
[[[[],[],[],[]],[]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => 2
[[[[[[[[]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => 6
[[],[],[],[],[],[],[],[]] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => 0
[[],[],[],[],[],[],[[]]] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,2,3,4,5,6,8,7] => 1
[[],[],[],[],[],[[]],[]] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8] => 1
[[],[],[],[[]],[],[],[]] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8] => 1
[[],[],[],[[]],[[]],[]] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => [1,2,3,5,4,7,6,8] => 1
[[],[],[],[[],[],[],[]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [1,2,3,5,6,7,8,4] => 1
[[],[],[[]],[[]],[],[]] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => [1,2,4,3,6,5,7,8] => 1
[[],[],[[[[],[],[]]]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [1,2,6,7,8,5,4,3] => 3
[[],[[]],[],[],[],[],[]] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => [1,3,2,4,5,6,7,8] => 1
[[],[[]],[],[],[[]],[]] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => [1,3,2,4,5,7,6,8] => 1
[[],[[]],[[]],[],[],[]] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => [1,3,2,5,4,6,7,8] => 1
[[],[[]],[[]],[[]],[]] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => [1,3,2,5,4,7,6,8] => 1
[[],[[],[]],[[],[]],[]] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => [1,3,4,2,6,7,5,8] => 1
[[],[[[]]],[[[]]],[]] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [1,4,3,2,7,6,5,8] => 2
[[],[[],[[],[[],[]]]]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [1,3,5,7,8,6,4,2] => 3
[[],[[[]],[[]],[[]]]] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => [1,4,3,6,5,8,7,2] => 2
[[],[[[]],[[[[]]]]]] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => [1,4,3,8,7,6,5,2] => 4
[[],[[[[[]]]],[[]]]] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => [1,6,5,4,3,8,7,2] => 4
[[],[[[[],[[[]]]]]]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [1,5,8,7,6,4,3,2] => 5
[[],[[[[[[]]],[]]]]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [1,7,6,5,8,4,3,2] => 5
[[],[[[[[],[],[]]]]]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [1,6,7,8,5,4,3,2] => 4
[[],[[[[[],[[]]]]]]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [1,6,8,7,5,4,3,2] => 5
[[],[[[[[[]],[]]]]]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => [1,7,6,8,5,4,3,2] => 5
[[],[[[[[[],[]]]]]]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [1,7,8,6,5,4,3,2] => 5
[[],[[[[[[[]]]]]]]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,8,7,6,5,4,3,2] => 6
[[[]],[],[],[],[],[],[]] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => 1
[[[]],[],[],[],[],[[]]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [2,1,3,4,5,6,8,7] => 1
[[[]],[[]],[[]],[[]]] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5,8,7] => 1
[[[]],[[]],[[],[[]]]] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => [2,1,4,3,6,8,7,5] => 2
[[[]],[[]],[[[]],[]]] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [2,1,4,3,7,6,8,5] => 2
[[[]],[[]],[[[[]]]]] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [2,1,4,3,8,7,6,5] => 3
[[[]],[[],[[]]],[[]]] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => [2,1,4,6,5,3,8,7] => 2
[[[]],[[[]],[]],[[]]] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [2,1,5,4,6,3,8,7] => 2
[[[]],[[[[]]]],[[]]] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [2,1,6,5,4,3,8,7] => 3
[[[]],[[[]],[[]],[]]] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => [2,1,5,4,7,6,8,3] => 2
[[[]],[[[[]],[]],[]]] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => [2,1,6,5,7,4,8,3] => 3
[[[]],[[[[[[]]]]]]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [2,1,8,7,6,5,4,3] => 5
[[[[]]],[],[],[],[],[]] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => 2
[[[],[]],[],[],[[],[]]] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => [2,3,1,4,5,7,8,6] => 1
[[[[]]],[],[],[[[]]]] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [3,2,1,4,5,8,7,6] => 2
[[[[]]],[[[]],[[]]]] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => [3,2,1,6,5,8,7,4] => 2
[[[[]]],[[[[[]]]]]] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [3,2,1,8,7,6,5,4] => 4
[[[[[]]]],[],[],[],[]] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => 3
[[[],[[]]],[[]],[[]]] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => [2,4,3,1,6,5,8,7] => 2
[[[[]],[]],[[]],[[]]] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => [3,2,4,1,6,5,8,7] => 2
[[[[[]]]],[[]],[[]]] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [4,3,2,1,6,5,8,7] => 3
[[[],[],[]],[[],[],[]]] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => [2,3,4,1,6,7,8,5] => 1
[[[],[[]]],[[],[[]]]] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => [2,4,3,1,6,8,7,5] => 2
[[[],[[]]],[[[]],[]]] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => [2,4,3,1,7,6,8,5] => 2
[[[[]],[]],[[],[[]]]] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => [3,2,4,1,6,8,7,5] => 2
[[[[]],[]],[[[]],[]]] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => [3,2,4,1,7,6,8,5] => 2
[[[[],[]]],[[[],[]]]] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => [3,4,2,1,7,8,6,5] => 2
[[[[[]]]],[[[[]]]]] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [4,3,2,1,8,7,6,5] => 3
[[[],[],[],[]],[],[],[]] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => 1
[[[[[[]]]]],[],[],[]] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => 4
[[[[]],[[]]],[[[]]]] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => [3,2,5,4,1,8,7,6] => 2
[[[[[[]]]]],[[[]]]] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => [5,4,3,2,1,8,7,6] => 4
[[[],[],[],[],[]],[],[]] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => [2,3,4,5,6,1,7,8] => 1
[[[[[[[]]]]]],[],[]] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => 5
[[[],[],[],[],[]],[[]]] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => [2,3,4,5,6,1,8,7] => 1
[[[[]],[[]],[]],[[]]] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => [3,2,5,4,6,1,8,7] => 2
[[[[[]],[]],[]],[[]]] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => [4,3,5,2,6,1,8,7] => 3
[[[[[[[]]]]]],[[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [6,5,4,3,2,1,8,7] => 5
[[[],[],[],[],[],[]],[]] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => [2,3,4,5,6,7,1,8] => 1
[[[[]],[[]],[[]]],[]] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => [3,2,5,4,7,6,1,8] => 2
[[[[]],[[[[]]]]],[]] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => [3,2,7,6,5,4,1,8] => 4
[[[[[[]]]],[[]]],[]] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => [5,4,3,2,7,6,1,8] => 4
[[[[[],[[[]]]]]],[]] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [4,7,6,5,3,2,1,8] => 5
[[[[[[[]]],[]]]],[]] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => 5
[[[[[[],[],[]]]]],[]] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => 4
[[[[[[],[[]]]]]],[]] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => [5,7,6,4,3,2,1,8] => 5
[[[[[[[]],[]]]]],[]] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => 5
[[[[[[[],[]]]]]],[]] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => 5
[[[[[[[[]]]]]]],[]] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => 6
[[[],[],[],[],[],[],[]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => 1
[[[],[],[[],[],[[]]]]] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [2,3,5,6,8,7,4,1] => 3
[[[],[[[[],[[]]]]]]] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [2,6,8,7,5,4,3,1] => 5
[[[[]],[],[],[],[],[]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => 2
[[[[]],[[]],[[]],[]]] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => [3,2,5,4,7,6,8,1] => 2
[[[[]],[[[]]],[[]]]] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => [3,2,6,5,4,8,7,1] => 3
[[[[]],[[[]],[]],[]]] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => [3,2,6,5,7,4,8,1] => 3
[[[[],[]],[],[],[],[]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1] => 2
[[[[[]]],[],[],[],[]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => 3
[[[[],[],[]],[],[],[]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1] => 2
[[[[[]],[]],[[]],[]]] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1] => 3
[[[[[]],[[]],[]],[]]] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => [4,3,6,5,7,2,8,1] => 3
[[[[[[]],[]],[]],[]]] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => 4
[[[[[[[]]]],[]],[]]] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => 5
[[[[[[[]],[]]]],[]]] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => 5
[[[[[[[[]]]]]],[]]] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => 6
[[[[],[[],[[[]]]]]]] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [3,5,8,7,6,4,2,1] => 5
[[[[[]],[[]],[[]]]]] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => [4,3,6,5,8,7,2,1] => 3
[[[[[[[]],[]],[]]]]] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => 5
[[[[[[[[]]]],[]]]]] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => 6
[[[[[[[]],[[]]]]]]] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => [6,5,8,7,4,3,2,1] => 5
[[[[[[[[]],[]]]]]]] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => 6
[[[[[[[[[]]]]]]]]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => 7
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 maximum drop size of a permutation.
The maximum drop size of a permutation $\pi$ of $[n]=\{1,2,\ldots, n\}$ is defined to be the maximum value of $i-\pi(i)$.
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
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.