- FindStat

edit this statistic or download as text // json

Identifier

St000409: Binary trees ⟶ ℤ

Values

[.,.] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 1884 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 number of pitchforks in a binary tree.
A pitchfork is a subtree of a complete binary tree with exactly three leaves, see Section 3.2 of [1].

References

[1] Disanto, F., Wiehe, T. Exact enumeration of cherries and pitchforks in ranked trees under the coalescent model MathSciNet:3068684

Code

def statistic(B):
    if B == BinaryTree() or B == BinaryTree([]):
        return 0
    if B == BinaryTree([[],None]) or B == BinaryTree([None, []]):
        return 1
    return sum(statistic(S) for S in B)

Created

Feb 25, 2016 at 09:05 by Martin Rubey

Updated

Dec 12, 2018 at 23:47 by Martin Rubey