- FindStat

Identifier

Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
St001737: Permutations ⟶ ℤ

Values

[.,.] => [1] => [1] => [1] => 0

[.,[.,.]] => [2,1] => [2,1] => [2,1] => 1

[[.,.],.] => [1,2] => [1,2] => [1,2] => 0

[.,[.,[.,.]]] => [3,2,1] => [2,3,1] => [3,2,1] => 1

[.,[[.,.],.]] => [2,3,1] => [3,2,1] => [2,3,1] => 1

[[.,.],[.,.]] => [1,3,2] => [1,3,2] => [1,3,2] => 1

[[.,[.,.]],.] => [2,1,3] => [2,1,3] => [2,1,3] => 1

[[[.,.],.],.] => [1,2,3] => [1,2,3] => [1,2,3] => 0

[.,[.,[.,[.,.]]]] => [4,3,2,1] => [2,3,4,1] => [4,2,3,1] => 1

[.,[.,[[.,.],.]]] => [3,4,2,1] => [2,4,3,1] => [3,2,4,1] => 2

[.,[[.,.],[.,.]]] => [2,4,3,1] => [3,2,4,1] => [2,4,3,1] => 1

[.,[[.,[.,.]],.]] => [3,2,4,1] => [4,3,2,1] => [3,4,1,2] => 1

[.,[[[.,.],.],.]] => [2,3,4,1] => [4,2,3,1] => [2,3,4,1] => 1

[[.,.],[.,[.,.]]] => [1,4,3,2] => [1,3,4,2] => [1,4,3,2] => 1

[[.,.],[[.,.],.]] => [1,3,4,2] => [1,4,3,2] => [1,3,4,2] => 1

[[.,[.,.]],[.,.]] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 2

[[[.,.],.],[.,.]] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1

[[.,[.,[.,.]]],.] => [3,2,1,4] => [2,3,1,4] => [3,2,1,4] => 1

[[.,[[.,.],.]],.] => [2,3,1,4] => [3,2,1,4] => [2,3,1,4] => 1

[[[.,.],[.,.]],.] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1

[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1

[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0

[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [2,3,4,5,1] => [5,2,3,4,1] => 1

[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [2,3,5,4,1] => [4,2,3,5,1] => 2

[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [2,4,3,5,1] => [3,2,5,4,1] => 2

[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [2,5,4,3,1] => [4,2,5,1,3] => 2

[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [2,5,3,4,1] => [3,2,4,5,1] => 2

[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [3,2,4,5,1] => [2,5,3,4,1] => 1

[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [3,2,5,4,1] => [2,4,3,5,1] => 2

[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [4,3,2,5,1] => [3,5,1,4,2] => 1

[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [4,2,3,5,1] => [2,3,5,4,1] => 1

[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [5,3,4,2,1] => [3,5,4,1,2] => 1

[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [5,4,3,2,1] => [3,4,5,1,2] => 1

[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [5,2,4,3,1] => [2,4,5,1,3] => 1

[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [5,3,2,4,1] => [3,4,1,5,2] => 2

[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [5,2,3,4,1] => [2,3,4,5,1] => 1

[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [1,3,4,5,2] => [1,5,3,4,2] => 1

[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [1,3,5,4,2] => [1,4,3,5,2] => 2

[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [1,4,3,5,2] => [1,3,5,4,2] => 1

[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [1,5,4,3,2] => [1,4,5,2,3] => 1

[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => 1

[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [2,1,4,5,3] => [2,1,5,4,3] => 2

[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => 2

[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,5,4,3] => 1

[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => 1

[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [2,3,1,5,4] => [3,2,1,5,4] => 2

[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => 2

[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => 2

[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => 2

[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => 1

[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [2,3,4,1,5] => [4,2,3,1,5] => 1

[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [2,4,3,1,5] => [3,2,4,1,5] => 2

[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [3,2,4,1,5] => [2,4,3,1,5] => 1

[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [4,3,2,1,5] => [3,4,1,2,5] => 1

[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [4,2,3,1,5] => [2,3,4,1,5] => 1

[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [1,3,4,2,5] => [1,4,3,2,5] => 1

[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => 1

[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => 2

[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1

[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => 1

[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => 1

[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1

[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => 1

[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0

[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => 1

[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => 2

[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [2,3,5,4,6,1] => [4,2,3,6,5,1] => 2

[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [2,3,6,5,4,1] => [5,2,3,6,1,4] => 2

[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [2,3,6,4,5,1] => [4,2,3,5,6,1] => 2

[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [2,4,3,5,6,1] => [3,2,6,4,5,1] => 2

[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [2,4,3,6,5,1] => [3,2,5,4,6,1] => 3

[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [2,5,4,3,6,1] => [4,2,6,1,5,3] => 2

[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [2,5,3,4,6,1] => [3,2,4,6,5,1] => 2

[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [2,6,4,5,3,1] => [4,2,6,5,1,3] => 2

[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [2,6,5,4,3,1] => [4,2,5,6,1,3] => 2

[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [2,6,3,5,4,1] => [3,2,5,6,1,4] => 2

[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [2,6,4,3,5,1] => [4,2,5,1,6,3] => 3

[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [2,6,3,4,5,1] => [3,2,4,5,6,1] => 2

[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [3,2,4,5,6,1] => [2,6,3,4,5,1] => 1

[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [3,2,4,6,5,1] => [2,5,3,4,6,1] => 2

[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [3,2,5,4,6,1] => [2,4,3,6,5,1] => 2

[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [3,2,6,5,4,1] => [2,5,3,6,1,4] => 2

[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [3,2,6,4,5,1] => [2,4,3,5,6,1] => 2

[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [4,3,2,5,6,1] => [3,6,1,4,5,2] => 1

[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [4,3,2,6,5,1] => [3,5,1,4,6,2] => 2

[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [4,2,3,5,6,1] => [2,3,6,4,5,1] => 1

[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [4,2,3,6,5,1] => [2,3,5,4,6,1] => 2

[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [5,3,4,2,6,1] => [3,6,4,1,5,2] => 1

[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [5,4,3,2,6,1] => [3,4,6,1,5,2] => 1

[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [5,2,4,3,6,1] => [2,4,6,1,5,3] => 1

[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [5,3,2,4,6,1] => [3,4,1,6,5,2] => 2

[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [5,2,3,4,6,1] => [2,3,4,6,5,1] => 1

[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [6,3,4,5,2,1] => [3,6,4,5,1,2] => 1

[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [6,3,5,4,2,1] => [3,5,4,6,1,2] => 2

[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [6,4,3,5,2,1] => [3,4,6,5,1,2] => 1

[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 1

[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [6,5,3,4,2,1] => [3,4,5,6,1,2] => 1

[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [6,2,4,5,3,1] => [2,4,6,5,1,3] => 1

[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [6,2,5,4,3,1] => [2,4,5,6,1,3] => 1

[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => 2

[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [6,2,3,5,4,1] => [2,3,5,6,1,4] => 1

>>> Load all 309 entries. <<<

[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [6,3,4,2,5,1] => [3,5,4,1,6,2] => 2

[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [6,4,3,2,5,1] => [3,4,5,1,6,2] => 2

[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [6,2,4,3,5,1] => [2,4,5,1,6,3] => 2

[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [6,3,2,4,5,1] => [3,4,1,5,6,2] => 2

[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [6,2,3,4,5,1] => [2,3,4,5,6,1] => 1

[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => 1

[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => 2

[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [1,3,5,4,6,2] => [1,4,3,6,5,2] => 2

[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [1,3,6,5,4,2] => [1,5,3,6,2,4] => 2

[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [1,3,6,4,5,2] => [1,4,3,5,6,2] => 2

[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [1,4,3,5,6,2] => [1,3,6,4,5,2] => 1

[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [1,4,3,6,5,2] => [1,3,5,4,6,2] => 2

[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [1,5,4,3,6,2] => [1,4,6,2,5,3] => 1

[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [1,5,3,4,6,2] => [1,3,4,6,5,2] => 1

[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [1,6,4,5,3,2] => [1,4,6,5,2,3] => 1

[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [1,6,5,4,3,2] => [1,4,5,6,2,3] => 1

[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [1,6,3,5,4,2] => [1,3,5,6,2,4] => 1

[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [1,6,4,3,5,2] => [1,4,5,2,6,3] => 2

[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [1,6,3,4,5,2] => [1,3,4,5,6,2] => 1

[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => 2

[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => 3

[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [2,1,5,4,6,3] => [2,1,4,6,5,3] => 2

[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => 2

[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [2,1,6,4,5,3] => [2,1,4,5,6,3] => 2

[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => 1

[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => 2

[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [1,2,5,4,6,3] => [1,2,4,6,5,3] => 1

[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [1,2,6,5,4,3] => [1,2,5,6,3,4] => 1

[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [1,2,6,4,5,3] => [1,2,4,5,6,3] => 1

[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => 2

[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => 2

[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [3,2,1,5,6,4] => [2,3,1,6,5,4] => 2

[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => 2

[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => 2

[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [1,3,2,6,5,4] => [1,3,2,5,6,4] => 2

[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => 2

[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [2,1,3,6,5,4] => [2,1,3,5,6,4] => 2

[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => 1

[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [1,2,3,6,5,4] => [1,2,3,5,6,4] => 1

[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => 2

[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => 3

[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [3,2,4,1,6,5] => [2,4,3,1,6,5] => 2

[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => 2

[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [4,2,3,1,6,5] => [2,3,4,1,6,5] => 2

[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => 2

[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [1,4,3,2,6,5] => [1,3,4,2,6,5] => 2

[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3

[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 2

[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => 2

[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [3,2,1,4,6,5] => [2,3,1,4,6,5] => 2

[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 2

[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => [2,1,3,4,6,5] => 2

[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 1

[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => 1

[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => 2

[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [2,4,3,5,1,6] => [3,2,5,4,1,6] => 2

[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [2,5,4,3,1,6] => [4,2,5,1,3,6] => 2

[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [2,5,3,4,1,6] => [3,2,4,5,1,6] => 2

[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [3,2,4,5,1,6] => [2,5,3,4,1,6] => 1

[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [3,2,5,4,1,6] => [2,4,3,5,1,6] => 2

[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [4,3,2,5,1,6] => [3,5,1,4,2,6] => 1

[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [4,2,3,5,1,6] => [2,3,5,4,1,6] => 1

[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [5,3,4,2,1,6] => [3,5,4,1,2,6] => 1

[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => 1

[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [5,2,4,3,1,6] => [2,4,5,1,3,6] => 1

[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [5,3,2,4,1,6] => [3,4,1,5,2,6] => 2

[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [5,2,3,4,1,6] => [2,3,4,5,1,6] => 1

[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => 1

[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => 2

[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [1,4,3,5,2,6] => [1,3,5,4,2,6] => 1

[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [1,5,4,3,2,6] => [1,4,5,2,3,6] => 1

[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [1,5,3,4,2,6] => [1,3,4,5,2,6] => 1

[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => 2

[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [2,1,5,4,3,6] => [2,1,4,5,3,6] => 2

[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => 1

[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [1,2,5,4,3,6] => [1,2,4,5,3,6] => 1

[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => 2

[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 2

[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 2

[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => [2,1,3,5,4,6] => 2

[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 1

[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => 1

[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => 2

[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [3,2,4,1,5,6] => [2,4,3,1,5,6] => 1

[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => 1

[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [4,2,3,1,5,6] => [2,3,4,1,5,6] => 1

[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => 1

[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [1,4,3,2,5,6] => [1,3,4,2,5,6] => 1

[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2

[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 1

[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => 1

[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 1

[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 1

[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1

[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0

[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [1,3,5,4,6,7,2] => [1,4,3,7,5,6,2] => 2

[[.,.],[.,[[.,.],[[.,.],.]]]] => [1,4,6,7,5,3,2] => [1,3,5,4,7,6,2] => [1,4,3,6,5,7,2] => 3

[[.,.],[.,[[[.,.],.],[.,.]]]] => [1,4,5,7,6,3,2] => [1,3,6,4,5,7,2] => [1,4,3,5,7,6,2] => 2

[[.,.],[.,[[[.,.],[.,.]],.]]] => [1,4,6,5,7,3,2] => [1,3,7,4,6,5,2] => [1,4,3,6,7,2,5] => 2

[[.,.],[.,[[[[.,.],.],.],.]]] => [1,4,5,6,7,3,2] => [1,3,7,4,5,6,2] => [1,4,3,5,6,7,2] => 2

[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [1,4,3,5,6,7,2] => [1,3,7,4,5,6,2] => 1

[[.,.],[[.,.],[.,[[.,.],.]]]] => [1,3,6,7,5,4,2] => [1,4,3,5,7,6,2] => [1,3,6,4,5,7,2] => 2

[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [1,4,3,6,5,7,2] => [1,3,5,4,7,6,2] => 2

[[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => [1,4,3,7,6,5,2] => [1,3,6,4,7,2,5] => 2

[[.,.],[[.,.],[[[.,.],.],.]]] => [1,3,5,6,7,4,2] => [1,4,3,7,5,6,2] => [1,3,5,4,6,7,2] => 2

[[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => [1,5,4,3,7,6,2] => [1,4,6,2,5,7,3] => 2

[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [1,5,3,4,6,7,2] => [1,3,4,7,5,6,2] => 1

[[.,.],[[[.,.],.],[[.,.],.]]] => [1,3,4,6,7,5,2] => [1,5,3,4,7,6,2] => [1,3,4,6,5,7,2] => 2

[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [1,6,5,4,3,7,2] => [1,4,5,7,2,6,3] => 1

[[.,.],[[[.,.],[.,.]],[.,.]]] => [1,3,5,4,7,6,2] => [1,6,3,5,4,7,2] => [1,3,5,7,2,6,4] => 1

[[.,.],[[[.,[.,.]],.],[.,.]]] => [1,4,3,5,7,6,2] => [1,6,4,3,5,7,2] => [1,4,5,2,7,6,3] => 2

[[.,.],[[[[.,.],.],.],[.,.]]] => [1,3,4,5,7,6,2] => [1,6,3,4,5,7,2] => [1,3,4,5,7,6,2] => 1

[[.,.],[[.,[[.,.],[.,.]]],.]] => [1,4,6,5,3,7,2] => [1,7,5,4,6,3,2] => [1,4,5,7,6,2,3] => 1

[[.,.],[[.,[[[.,.],.],.]],.]] => [1,4,5,6,3,7,2] => [1,7,6,4,5,3,2] => [1,4,5,6,7,2,3] => 1

[[.,.],[[[.,.],[.,[.,.]]],.]] => [1,3,6,5,4,7,2] => [1,7,3,5,6,4,2] => [1,3,5,7,6,2,4] => 1

[[.,.],[[[.,.],[[.,.],.]],.]] => [1,3,5,6,4,7,2] => [1,7,3,6,5,4,2] => [1,3,5,6,7,2,4] => 1

[[.,.],[[[.,[.,.]],[.,.]],.]] => [1,4,3,6,5,7,2] => [1,7,4,3,6,5,2] => [1,4,6,2,7,3,5] => 2

[[.,.],[[[[.,.],.],[.,.]],.]] => [1,3,4,6,5,7,2] => [1,7,3,4,6,5,2] => [1,3,4,6,7,2,5] => 1

[[.,.],[[[.,[.,[.,.]]],.],.]] => [1,5,4,3,6,7,2] => [1,7,4,5,3,6,2] => [1,4,6,5,2,7,3] => 2

[[.,.],[[[.,[[.,.],.]],.],.]] => [1,4,5,3,6,7,2] => [1,7,5,4,3,6,2] => [1,4,5,6,2,7,3] => 2

[[.,.],[[[[.,.],[.,.]],.],.]] => [1,3,5,4,6,7,2] => [1,7,3,5,4,6,2] => [1,3,5,6,2,7,4] => 2

[[.,.],[[[[.,[.,.]],.],.],.]] => [1,4,3,5,6,7,2] => [1,7,4,3,5,6,2] => [1,4,5,2,6,7,3] => 2

[[.,.],[[[[[.,.],.],.],.],.]] => [1,3,4,5,6,7,2] => [1,7,3,4,5,6,2] => [1,3,4,5,6,7,2] => 1

[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => 1

[[[.,.],.],[.,[.,[[.,.],.]]]] => [1,2,6,7,5,4,3] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => 2

[[[.,.],.],[.,[[.,.],[.,.]]]] => [1,2,5,7,6,4,3] => [1,2,4,6,5,7,3] => [1,2,5,4,7,6,3] => 2

[[[.,.],.],[.,[[.,[.,.]],.]]] => [1,2,6,5,7,4,3] => [1,2,4,7,6,5,3] => [1,2,6,4,7,3,5] => 2

[[[.,.],.],[.,[[[.,.],.],.]]] => [1,2,5,6,7,4,3] => [1,2,4,7,5,6,3] => [1,2,5,4,6,7,3] => 2

[[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => [1,2,5,4,6,7,3] => [1,2,4,7,5,6,3] => 1

[[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => [1,2,5,4,7,6,3] => [1,2,4,6,5,7,3] => 2

[[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => [1,2,6,5,4,7,3] => [1,2,5,7,3,6,4] => 1

[[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => [1,2,6,4,5,7,3] => [1,2,4,5,7,6,3] => 1

[[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => [1,2,7,5,6,4,3] => [1,2,5,7,6,3,4] => 1

[[[.,.],.],[[.,[[.,.],.]],.]] => [1,2,5,6,4,7,3] => [1,2,7,6,5,4,3] => [1,2,5,6,7,3,4] => 1

[[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => [1,2,7,4,6,5,3] => [1,2,4,6,7,3,5] => 1

[[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => [1,2,7,5,4,6,3] => [1,2,5,6,3,7,4] => 2

[[[.,.],.],[[[[.,.],.],.],.]] => [1,2,4,5,6,7,3] => [1,2,7,4,5,6,3] => [1,2,4,5,6,7,3] => 1

[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => 2

[[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => 3

[[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => [1,3,2,6,5,7,4] => [1,3,2,5,7,6,4] => 2

[[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => [1,3,2,7,6,5,4] => [1,3,2,6,7,4,5] => 2

[[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => [1,3,2,7,5,6,4] => [1,3,2,5,6,7,4] => 2

[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => 1

[[[[.,.],.],.],[.,[[.,.],.]]] => [1,2,3,6,7,5,4] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => 2

[[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => [1,2,3,6,5,7,4] => [1,2,3,5,7,6,4] => 1

[[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => [1,2,3,7,6,5,4] => [1,2,3,6,7,4,5] => 1

[[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => [1,2,3,7,5,6,4] => [1,2,3,5,6,7,4] => 1

[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => 2

[[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => 2

[[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => [1,4,3,2,6,7,5] => [1,3,4,2,7,6,5] => 2

[[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => [1,4,3,2,7,6,5] => [1,3,4,2,6,7,5] => 2

[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => 2

[[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => [1,2,4,3,7,6,5] => [1,2,4,3,6,7,5] => 2

[[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => 2

[[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => [1,3,2,4,7,6,5] => [1,3,2,4,6,7,5] => 2

[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => 1

[[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => [1,2,3,4,7,6,5] => [1,2,3,4,6,7,5] => 1

[[[.,.],[.,[[.,.],.]]],[.,.]] => [1,4,5,3,2,7,6] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => 3

[[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => [1,4,3,5,2,7,6] => [1,3,5,4,2,7,6] => 2

[[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => [1,5,4,3,2,7,6] => [1,4,5,2,3,7,6] => 2

[[[.,.],[[[.,.],.],.]],[.,.]] => [1,3,4,5,2,7,6] => [1,5,3,4,2,7,6] => [1,3,4,5,2,7,6] => 2

[[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => 2

[[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => [1,2,5,4,3,7,6] => [1,2,4,5,3,7,6] => 2

[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => [1,3,2,5,4,7,6] => 3

[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => 2

[[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => 2

[[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => [1,4,3,2,5,7,6] => [1,3,4,2,5,7,6] => 2

[[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => 2

[[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => [1,3,2,4,5,7,6] => 2

[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => 1

[[[.,.],[.,[[.,.],[.,.]]]],.] => [1,4,6,5,3,2,7] => [1,3,5,4,6,2,7] => [1,4,3,6,5,2,7] => 2

[[[.,.],[.,[[[.,.],.],.]]],.] => [1,4,5,6,3,2,7] => [1,3,6,4,5,2,7] => [1,4,3,5,6,2,7] => 2

[[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => [1,4,3,5,6,2,7] => [1,3,6,4,5,2,7] => 1

[[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => [1,4,3,6,5,2,7] => [1,3,5,4,6,2,7] => 2

[[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => [1,5,4,3,6,2,7] => [1,4,6,2,5,3,7] => 1

[[[.,.],[[[.,.],.],[.,.]]],.] => [1,3,4,6,5,2,7] => [1,5,3,4,6,2,7] => [1,3,4,6,5,2,7] => 1

[[[.,.],[[.,[.,[.,.]]],.]],.] => [1,5,4,3,6,2,7] => [1,6,4,5,3,2,7] => [1,4,6,5,2,3,7] => 1

[[[.,.],[[.,[[.,.],.]],.]],.] => [1,4,5,3,6,2,7] => [1,6,5,4,3,2,7] => [1,4,5,6,2,3,7] => 1

[[[.,.],[[[.,.],[.,.]],.]],.] => [1,3,5,4,6,2,7] => [1,6,3,5,4,2,7] => [1,3,5,6,2,4,7] => 1

[[[.,.],[[[.,[.,.]],.],.]],.] => [1,4,3,5,6,2,7] => [1,6,4,3,5,2,7] => [1,4,5,2,6,3,7] => 2

[[[.,.],[[[[.,.],.],.],.]],.] => [1,3,4,5,6,2,7] => [1,6,3,4,5,2,7] => [1,3,4,5,6,2,7] => 1

[[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => 1

[[[[.,.],.],[.,[[.,.],.]]],.] => [1,2,5,6,4,3,7] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => 2

[[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => [1,2,5,4,6,3,7] => [1,2,4,6,5,3,7] => 1

[[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => [1,2,6,5,4,3,7] => [1,2,5,6,3,4,7] => 1

[[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => [1,2,6,4,5,3,7] => [1,2,4,5,6,3,7] => 1

[[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => 2

[[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => [1,3,2,6,5,4,7] => [1,3,2,5,6,4,7] => 2

[[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => 1

[[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => [1,2,3,6,5,4,7] => [1,2,3,5,6,4,7] => 1

[[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => 2

[[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => [1,4,3,2,6,5,7] => [1,3,4,2,6,5,7] => 2

[[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => 2

[[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => [1,3,2,4,6,5,7] => 2

[[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => 1

[[[[.,.],[.,[[.,.],.]]],.],.] => [1,4,5,3,2,6,7] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => 2

[[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => [1,4,3,5,2,6,7] => [1,3,5,4,2,6,7] => 1

[[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => [1,5,4,3,2,6,7] => [1,4,5,2,3,6,7] => 1

[[[[.,.],[[[.,.],.],.]],.],.] => [1,3,4,5,2,6,7] => [1,5,3,4,2,6,7] => [1,3,4,5,2,6,7] => 1

[[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => 1

[[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => [1,2,5,4,3,6,7] => [1,2,4,5,3,6,7] => 1

[[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => [1,3,2,5,4,6,7] => 2

[[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => 1

[[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => 1

[[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => [1,4,3,2,5,6,7] => [1,3,4,2,5,6,7] => 1

[[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => 1

[[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => [1,3,2,4,5,6,7] => 1

[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 4\ q$

$F_{4} = 1 + 11\ q + 2\ q^{2}$

$F_{5} = 1 + 26\ q + 15\ q^{2}$

$F_{6} = 1 + 57\ q + 69\ q^{2} + 5\ q^{3}$

Description

The number of descents of type 2 in a permutation.
A position

$i\in[1,n-1]$ is a descent of type 2 of a permutation

$\pi$ of

$n$ letters, if it is a descent and if

$\pi(j) < \pi(i)$ for all

$j < i$ .

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.

Map

Corteel

Description

Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.

Map

descent views to invisible inversion bottoms

Description

Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation

$\sigma$ is a pair

$i < j$ such that

$i < \sigma(j) < \sigma(i)$ . The element

$\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation

$\pi$ is an element

$\pi(j)$ such that

$\pi(i+1) < \pi(j) < \pi(i)$ , and additionally the smallest element in the decreasing run containing

$\pi(i)$ is smaller than the smallest element in the decreasing run containing

$\pi(j)$ .
This map is a bijection

$\chi:\mathfrak S_n \to \mathfrak S_n$ , such that

the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$ ,
the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$ ,
the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$ ,
the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$ , and
the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$ .