Identifier
Values
[.,.] => [.,.] => [1] => 1
[.,[.,.]] => [.,[.,.]] => [2,1] => 1
[[.,.],.] => [[.,.],.] => [1,2] => 1
[.,[.,[.,.]]] => [.,[.,[.,.]]] => [3,2,1] => 1
[.,[[.,.],.]] => [.,[[.,.],.]] => [2,3,1] => 2
[[.,.],[.,.]] => [[.,[.,.]],.] => [2,1,3] => 1
[[.,[.,.]],.] => [[.,.],[.,.]] => [1,3,2] => 2
[[[.,.],.],.] => [[[.,.],.],.] => [1,2,3] => 1
[.,[.,[.,[.,.]]]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 1
[.,[.,[[.,.],.]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => 2
[.,[[.,.],[.,.]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => 2
[.,[[.,[.,.]],.]] => [.,[[.,.],[.,.]]] => [2,4,3,1] => 2
[.,[[[.,.],.],.]] => [.,[[[.,.],.],.]] => [2,3,4,1] => 2
[[.,.],[.,[.,.]]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 1
[[.,.],[[.,.],.]] => [[.,[[.,.],.]],.] => [2,3,1,4] => 2
[[.,[.,.]],[.,.]] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 2
[[[.,.],.],[.,.]] => [[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[.,[.,[.,.]]],.] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 2
[[.,[[.,.],.]],.] => [[.,.],[[.,.],.]] => [1,3,4,2] => 2
[[[.,.],[.,.]],.] => [[[.,.],[.,.]],.] => [1,3,2,4] => 2
[[[.,[.,.]],.],.] => [[[.,.],.],[.,.]] => [1,2,4,3] => 2
[[[[.,.],.],.],.] => [[[[.,.],.],.],.] => [1,2,3,4] => 1
[.,[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 1
[.,[.,[.,[[.,.],.]]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => 2
[.,[.,[[.,.],[.,.]]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => 2
[.,[.,[[.,[.,.]],.]]] => [.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => 2
[.,[.,[[[.,.],.],.]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => 2
[.,[[.,.],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => 2
[.,[[.,.],[[.,.],.]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => 3
[.,[[.,[.,.]],[.,.]]] => [.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => 2
[.,[[[.,.],.],[.,.]]] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => 2
[.,[[.,[.,[.,.]]],.]] => [.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => 2
[.,[[.,[[.,.],.]],.]] => [.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => 2
[.,[[[.,.],[.,.]],.]] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => 3
[.,[[[.,[.,.]],.],.]] => [.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => 2
[.,[[[[.,.],.],.],.]] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => 2
[[.,.],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 1
[[.,.],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => 2
[[.,.],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => 2
[[.,.],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => 2
[[.,.],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => 2
[[.,[.,.]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 2
[[.,[.,.]],[[.,.],.]] => [[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => 3
[[[.,.],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 1
[[[.,.],.],[[.,.],.]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => 2
[[.,[.,[.,.]]],[.,.]] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 2
[[.,[[.,.],.]],[.,.]] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 2
[[[.,.],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 2
[[[.,[.,.]],.],[.,.]] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 2
[[[[.,.],.],.],[.,.]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[.,[.,[.,[.,.]]]],.] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 2
[[.,[.,[[.,.],.]]],.] => [[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => 2
[[.,[[.,.],[.,.]]],.] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 3
[[.,[[.,[.,.]],.]],.] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 2
[[.,[[[.,.],.],.]],.] => [[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => 2
[[[.,.],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 2
[[[.,.],[[.,.],.]],.] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 2
[[[.,[.,.]],[.,.]],.] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 3
[[[[.,.],.],[.,.]],.] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 2
[[[.,[.,[.,.]]],.],.] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 2
[[[.,[[.,.],.]],.],.] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 2
[[[[.,.],[.,.]],.],.] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 2
[[[[.,[.,.]],.],.],.] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 2
[[[[[.,.],.],.],.],.] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => 2
[.,[.,[.,[[.,.],[.,.]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => 3
[.,[.,[[[.,[.,.]],.],.]]] => [.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => 2
[.,[.,[[[[.,.],.],.],.]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => 2
[.,[[.,.],[.,[[.,.],.]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => 3
[.,[[.,.],[[.,.],[.,.]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => 3
[.,[[.,.],[[.,[.,.]],.]]] => [.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => 3
[.,[[.,.],[[[.,.],.],.]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => 3
[.,[[.,[.,.]],[.,[.,.]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => 2
[.,[[.,[.,.]],[[.,.],.]]] => [.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => 3
[.,[[[.,.],.],[.,[.,.]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => 2
[.,[[[.,.],.],[[.,.],.]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => 3
[.,[[.,[.,[.,.]]],[.,.]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => 2
[.,[[.,[[.,.],.]],[.,.]]] => [.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => 2
[.,[[[.,.],[.,.]],[.,.]]] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => 3
[.,[[[.,[.,.]],.],[.,.]]] => [.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => 2
[.,[[[[.,.],.],.],[.,.]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => 2
[.,[[.,[.,[[.,.],.]]],.]] => [.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => 3
[.,[[.,[[.,[.,.]],.]],.]] => [.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => 2
[.,[[.,[[[.,.],.],.]],.]] => [.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => 2
[.,[[[.,.],[.,[.,.]]],.]] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => 3
[.,[[[.,.],[[.,.],.]],.]] => [.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => 3
[.,[[[.,[.,.]],[.,.]],.]] => [.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => 3
[.,[[[[.,.],.],[.,.]],.]] => [.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => 3
>>> Load all 196 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => 2
[.,[[[.,[[.,.],.]],.],.]] => [.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => 2
[.,[[[[.,.],[.,.]],.],.]] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => 3
[.,[[[[.,[.,.]],.],.],.]] => [.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => 2
[.,[[[[[.,.],.],.],.],.]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => 2
[[.,.],[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => 2
[[.,.],[.,[[[.,.],.],.]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => 2
[[.,.],[[.,.],[[.,.],.]]] => [[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => 3
[[.,.],[[.,[.,.]],[.,.]]] => [[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => 2
[[.,.],[[[.,.],.],[.,.]]] => [[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => 2
[[.,.],[[.,[[.,.],.]],.]] => [[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => 2
[[.,.],[[[.,.],[.,.]],.]] => [[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => 3
[[.,.],[[[.,[.,.]],.],.]] => [[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => 2
[[.,.],[[[[.,.],.],.],.]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => 3
[[.,[.,.]],[[.,.],[.,.]]] => [[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => 3
[[.,[.,.]],[[.,[.,.]],.]] => [[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => 3
[[.,[.,.]],[[[.,.],.],.]] => [[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => 3
[[[.,.],.],[.,[.,[.,.]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 1
[[[.,.],.],[.,[[.,.],.]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => 2
[[[.,.],.],[[.,.],[.,.]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => 2
[[[.,.],.],[[.,[.,.]],.]] => [[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => 2
[[[.,.],.],[[[.,.],.],.]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => 3
[[.,[[.,.],.]],[.,[.,.]]] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 2
[[.,[[.,.],.]],[[.,.],.]] => [[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => 3
[[[.,.],[.,.]],[.,[.,.]]] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 2
[[[.,.],[.,.]],[[.,.],.]] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => 3
[[[.,[.,.]],.],[.,[.,.]]] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 2
[[[.,[.,.]],.],[[.,.],.]] => [[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => 3
[[[[.,.],.],.],[.,[.,.]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 1
[[[[.,.],.],.],[[.,.],.]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 2
[[.,[[.,.],[.,.]]],[.,.]] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 3
[[.,[[.,[.,.]],.]],[.,.]] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 2
[[.,[[[.,.],.],.]],[.,.]] => [[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 2
[[[.,.],[[.,.],.]],[.,.]] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 2
[[[.,[.,.]],[.,.]],[.,.]] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 3
[[[[.,.],.],[.,.]],[.,.]] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 2
[[[.,[.,[.,.]]],.],[.,.]] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 2
[[[.,[[.,.],.]],.],[.,.]] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 2
[[[[.,.],[.,.]],.],[.,.]] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 2
[[[[.,[.,.]],.],.],[.,.]] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 2
[[[[[.,.],.],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 2
[[.,[.,[.,[[.,.],.]]]],.] => [[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => 3
[[.,[.,[[.,[.,.]],.]]],.] => [[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => 2
[[.,[.,[[[.,.],.],.]]],.] => [[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 3
[[.,[[.,.],[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => 3
[[.,[[.,[.,.]],[.,.]]],.] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 3
[[.,[[[.,.],.],[.,.]]],.] => [[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => 3
[[.,[[.,[.,[.,.]]],.]],.] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 2
[[.,[[.,[[.,.],.]],.]],.] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 2
[[.,[[[.,.],[.,.]],.]],.] => [[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => 3
[[.,[[[.,[.,.]],.],.]],.] => [[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => 2
[[.,[[[[.,.],.],.],.]],.] => [[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => 2
[[[.,.],[.,[.,[.,.]]]],.] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 2
[[[.,.],[.,[[.,.],.]]],.] => [[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => 2
[[[.,.],[[.,.],[.,.]]],.] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 3
[[[.,.],[[.,[.,.]],.]],.] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 2
[[[.,.],[[[.,.],.],.]],.] => [[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => 2
[[[.,[.,.]],[.,[.,.]]],.] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 3
[[[.,[.,.]],[[.,.],.]],.] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 3
[[[[.,.],.],[.,[.,.]]],.] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 2
[[[[.,.],.],[[.,.],.]],.] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 2
[[[.,[.,[.,.]]],[.,.]],.] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 3
[[[.,[[.,.],.]],[.,.]],.] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 3
[[[[.,.],[.,.]],[.,.]],.] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 3
[[[[.,[.,.]],.],[.,.]],.] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 3
[[[[[.,.],.],.],[.,.]],.] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 2
[[[.,[.,[.,[.,.]]]],.],.] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 2
[[[.,[.,[[.,.],.]]],.],.] => [[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => 2
[[[.,[[.,.],[.,.]]],.],.] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 3
[[[.,[[.,[.,.]],.]],.],.] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 2
[[[.,[[[.,.],.],.]],.],.] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 2
[[[[.,.],[.,[.,.]]],.],.] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 2
[[[[.,.],[[.,.],.]],.],.] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 2
[[[[.,[.,.]],[.,.]],.],.] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 3
[[[[[.,.],.],[.,.]],.],.] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 2
[[[[.,[.,[.,.]]],.],.],.] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 2
[[[[.,[[.,.],.]],.],.],.] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 2
[[[[[.,.],[.,.]],.],.],.] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 2
[[[[[.,[.,.]],.],.],.],.] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 2
[[[[[[.,.],.],.],.],.],.] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 1
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Description
The number of valleys of a permutation, including the boundary.
The number of valleys excluding the boundary is St000353The number of inner valleys of a permutation..
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
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.