- FindStat

Identifier

Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
St000203: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of external nodes of a binary tree.
That is, the number of nodes that can be reached from the root by only left steps or only right steps, plus $1$ for the root node itself. A counting formula for the number of external node in all binary trees of size $n$ can be found in [1].

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.