- FindStat

Identifier

Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
St000167: Ordered trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 260 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [[],[],[],[],[],[],[],[]] => 8

[[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[[],[],[],[],[],[],[]]] => 7

[[1,3,4,5,6,7],[2],[8]] => [8,2,1,3,4,5,6,7] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [[[[]],[],[],[],[],[]]] => 6

[[1,2,4,5,6,7],[3],[8]] => [8,3,1,2,4,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[[],[]],[],[],[],[]]] => 6

[[1,2,4,5,8],[3,6],[7]] => [7,3,6,1,2,4,5,8] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => [[[[],[]],[[],[]]],[]] => 5

[[1,2,5,6,7],[3,4],[8]] => [8,3,4,1,2,5,6,7] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [[[[],[]],[],[],[],[]]] => 6

[[1,2,4,6,8],[3],[5],[7]] => [7,5,3,1,2,4,6,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[],[]],[]],[]],[]] => 5

[[1,4,5,6,7],[2],[3],[8]] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [[[[[]]],[],[],[],[]]] => 5

[[1,2,6,7],[3,4],[5,8]] => [5,8,3,4,1,2,6,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[[[],[]],[]],[[],[]]] => 5

[[1,2,4,7],[3,6],[5,8]] => [5,8,3,6,1,2,4,7] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[[[],[]],[]],[[],[]]] => 5

[[1,2,4,8],[3,6],[5],[7]] => [7,5,3,6,1,2,4,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[],[]],[]],[]],[]] => 5

[[1,2,4,6],[3,8],[5],[7]] => [7,5,3,8,1,2,4,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[],[]],[]],[]],[]] => 5

[[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[[[],[],[]]]]],[]] => 4

[[1,2,4],[3,6,7],[5,8]] => [5,8,3,6,7,1,2,4] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => [[[[],[]],[]],[[],[]]] => 5

[[1,2,4],[3,6,8],[5],[7]] => [7,5,3,6,8,1,2,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[],[]],[]],[]],[]] => 5

[[1,2,3],[4,8],[5],[6],[7]] => [7,6,5,4,8,1,2,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [[[[[[],[],[]]]]],[]] => 4

[[1,4,8],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [[[[[[[]]],[]]]],[]] => 3

[[1,3,8],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[[[[[[]],[]]]]],[]] => 3

[[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[[[[[],[]]]]]],[]] => 3

[[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[],[]],[]],[]],[]] => 5

[[1,3],[2,8],[4],[5],[6],[7]] => [7,6,5,4,2,8,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [[[[[[[]],[]]]]],[]] => 3

[[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [[[[[[[],[]]]]]],[]] => 3

[[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [[[[[[[[]]]]]]],[]] => 2

[[1,2,3,4,5,6,7,8,9]] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [[],[],[],[],[],[],[],[],[]] => 9

[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [[[],[],[],[],[],[],[],[]]] => 8

[[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [[],[],[],[],[],[],[],[],[],[]] => 10

[[1,2,3,4,5,6,7,8,9],[10]] => [10,1,2,3,4,5,6,7,8,9] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [[[],[],[],[],[],[],[],[],[]]] => 9

[[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[],[]],[]],[]],[]],[]] => 6

[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => [[[[[[[],[]],[]],[]],[]],[]],[]] => 7

[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[]]]]]]]],[]] => 2

[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [[[[[[[[[[]]]]]]]]],[]] => 2

[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [[[[[[[[],[]]]]]]],[]] => 3

[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2,10] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => [[[[[[[[[],[]]]]]]]],[]] => 3

[[1,3,4,5,6,7,8],[2],[9]] => [9,2,1,3,4,5,6,7,8] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [[[[]],[],[],[],[],[],[]]] => 7

[[1,2],[3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,9,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => [[[[[[[[],[]]]]]]],[]] => 3

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = q + 2\ q^{2} + q^{3}$

$F_{4} = q + 4\ q^{2} + 4\ q^{3} + q^{4}$

$F_{5} = q + 6\ q^{2} + 12\ q^{3} + 6\ q^{4} + q^{5}$

$F_{6} = q + 9\ q^{2} + 28\ q^{3} + 28\ q^{4} + 9\ q^{5} + q^{6}$

Description

The number of leaves of an ordered tree.
This is the number of nodes which do not have any children.

Map

to ordered tree: right child = right brother

Description

Return an ordered tree of size

$n+1$ by the following recursive rule:

if $x$ is the right child of $y$ , $x$ becomes the right brother of $y$ ,
if $x$ is the left child of $y$ , $x$ becomes the first child of $y$ .

Map

binary search tree: left to right

Description

Return the shape of the binary search tree of the permutation as a non labelled binary tree.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.