- FindStat

Identifier

Mp00080: Set partitions —to permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000128: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 5$

$F_{4} = 15$

$F_{5} = 52$

$F_{6} = 199 + 4\ q$

$F_{7} = 827 + 50\ q$

Description

The number of occurrences of the contiguous pattern [.,[.,[[.,[.,.]],.]]] in a binary tree.
oeis:A159769 counts binary trees avoiding this pattern.

Map

to permutation

Description

Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.

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.