- FindStat

edit this statistic or download as text // json

Identifier

St000414: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

[.,[.,[.,[.,.]]]] => 3

[.,[.,[[.,.],.]]] => 3

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

[.,[[.,[.,.]],.]] => 3

[.,[[[.,.],.],.]] => 3

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

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

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

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

[[.,[.,[.,.]]],.] => 3

[[.,[[.,.],.]],.] => 3

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

[[[.,[.,.]],.],.] => 3

[[[[.,.],.],.],.] => 3

[.,[.,[.,[.,[.,.]]]]] => 4

[.,[.,[.,[[.,.],.]]]] => 4

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

[.,[.,[[.,[.,.]],.]]] => 4

[.,[.,[[[.,.],.],.]]] => 4

[.,[[.,.],[.,[.,.]]]] => 3

[.,[[.,.],[[.,.],.]]] => 3

[.,[[.,[.,.]],[.,.]]] => 3

[.,[[[.,.],.],[.,.]]] => 3

[.,[[.,[.,[.,.]]],.]] => 4

[.,[[.,[[.,.],.]],.]] => 4

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

[.,[[[.,[.,.]],.],.]] => 4

[.,[[[[.,.],.],.],.]] => 4

[[.,.],[.,[.,[.,.]]]] => 3

[[.,.],[.,[[.,.],.]]] => 3

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

[[.,.],[[.,[.,.]],.]] => 3

[[.,.],[[[.,.],.],.]] => 3

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

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

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

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

[[.,[.,[.,.]]],[.,.]] => 3

[[.,[[.,.],.]],[.,.]] => 3

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

[[[.,[.,.]],.],[.,.]] => 3

[[[[.,.],.],.],[.,.]] => 3

[[.,[.,[.,[.,.]]]],.] => 4

[[.,[.,[[.,.],.]]],.] => 4

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

[[.,[[.,[.,.]],.]],.] => 4

[[.,[[[.,.],.],.]],.] => 4

[[[.,.],[.,[.,.]]],.] => 3

[[[.,.],[[.,.],.]],.] => 3

[[[.,[.,.]],[.,.]],.] => 3

[[[[.,.],.],[.,.]],.] => 3

[[[.,[.,[.,.]]],.],.] => 4

[[[.,[[.,.],.]],.],.] => 4

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

[[[[.,[.,.]],.],.],.] => 4

[[[[[.,.],.],.],.],.] => 4

[.,[.,[.,[.,[.,[.,.]]]]]] => 5

[.,[.,[.,[.,[[.,.],.]]]]] => 5

[.,[.,[.,[[.,.],[.,.]]]]] => 3

[.,[.,[.,[[.,[.,.]],.]]]] => 5

[.,[.,[.,[[[.,.],.],.]]]] => 5

[.,[.,[[.,.],[.,[.,.]]]]] => 4

[.,[.,[[.,.],[[.,.],.]]]] => 4

[.,[.,[[.,[.,.]],[.,.]]]] => 4

[.,[.,[[[.,.],.],[.,.]]]] => 4

[.,[.,[[.,[.,[.,.]]],.]]] => 5

[.,[.,[[.,[[.,.],.]],.]]] => 5

[.,[.,[[[.,.],[.,.]],.]]] => 3

[.,[.,[[[.,[.,.]],.],.]]] => 5

[.,[.,[[[[.,.],.],.],.]]] => 5

[.,[[.,.],[.,[.,[.,.]]]]] => 4

[.,[[.,.],[.,[[.,.],.]]]] => 4

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

[.,[[.,.],[[.,[.,.]],.]]] => 4

[.,[[.,.],[[[.,.],.],.]]] => 4

[.,[[.,[.,.]],[.,[.,.]]]] => 3

[.,[[.,[.,.]],[[.,.],.]]] => 3

[.,[[[.,.],.],[.,[.,.]]]] => 3

[.,[[[.,.],.],[[.,.],.]]] => 3

[.,[[.,[.,[.,.]]],[.,.]]] => 4

[.,[[.,[[.,.],.]],[.,.]]] => 4

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

[.,[[[.,[.,.]],.],[.,.]]] => 4

[.,[[[[.,.],.],.],[.,.]]] => 4

[.,[[.,[.,[.,[.,.]]]],.]] => 5

[.,[[.,[.,[[.,.],.]]],.]] => 5

[.,[[.,[[.,.],[.,.]]],.]] => 3

[.,[[.,[[.,[.,.]],.]],.]] => 5

[.,[[.,[[[.,.],.],.]],.]] => 5

[.,[[[.,.],[.,[.,.]]],.]] => 4

[.,[[[.,.],[[.,.],.]],.]] => 4

[.,[[[.,[.,.]],[.,.]],.]] => 4

[.,[[[[.,.],.],[.,.]],.]] => 4

[.,[[[.,[.,[.,.]]],.],.]] => 5

>>> Load all 1200 entries. <<<

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

Description

The binary logarithm of the number of binary trees with the same underlying unordered tree.

Code

@cached_function
def Binary_to_Rooted(n):
    return [RootedTree(S) for S in BinaryTrees(n)]

def statistic(tree):
    T = RootedTree(tree)
    return ZZ(Binary_to_Rooted(tree.node_number()).count(T)).log(2)

Created

Feb 25, 2016 at 11:21 by Martin Rubey

Updated

Mar 31, 2019 at 22:32 by Martin Rubey