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Identifier

St000412: Binary trees ⟶ ℤ

Values

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

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

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

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

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

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

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

[.,[.,[.,[.,.]]]] => 8

[.,[.,[[.,.],.]]] => 8

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

[.,[[.,[.,.]],.]] => 8

[.,[[[.,.],.],.]] => 8

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

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

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

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

[[.,[.,[.,.]]],.] => 8

[[.,[[.,.],.]],.] => 8

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

[[[.,[.,.]],.],.] => 8

[[[[.,.],.],.],.] => 8

[.,[.,[.,[.,[.,.]]]]] => 16

[.,[.,[.,[[.,.],.]]]] => 16

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

[.,[.,[[.,[.,.]],.]]] => 16

[.,[.,[[[.,.],.],.]]] => 16

[.,[[.,.],[.,[.,.]]]] => 8

[.,[[.,.],[[.,.],.]]] => 8

[.,[[.,[.,.]],[.,.]]] => 8

[.,[[[.,.],.],[.,.]]] => 8

[.,[[.,[.,[.,.]]],.]] => 16

[.,[[.,[[.,.],.]],.]] => 16

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

[.,[[[.,[.,.]],.],.]] => 16

[.,[[[[.,.],.],.],.]] => 16

[[.,.],[.,[.,[.,.]]]] => 8

[[.,.],[.,[[.,.],.]]] => 8

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

[[.,.],[[.,[.,.]],.]] => 8

[[.,.],[[[.,.],.],.]] => 8

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

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

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

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

[[.,[.,[.,.]]],[.,.]] => 8

[[.,[[.,.],.]],[.,.]] => 8

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

[[[.,[.,.]],.],[.,.]] => 8

[[[[.,.],.],.],[.,.]] => 8

[[.,[.,[.,[.,.]]]],.] => 16

[[.,[.,[[.,.],.]]],.] => 16

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

[[.,[[.,[.,.]],.]],.] => 16

[[.,[[[.,.],.],.]],.] => 16

[[[.,.],[.,[.,.]]],.] => 8

[[[.,.],[[.,.],.]],.] => 8

[[[.,[.,.]],[.,.]],.] => 8

[[[[.,.],.],[.,.]],.] => 8

[[[.,[.,[.,.]]],.],.] => 16

[[[.,[[.,.],.]],.],.] => 16

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

[[[[.,[.,.]],.],.],.] => 16

[[[[[.,.],.],.],.],.] => 16

[.,[.,[.,[.,[.,[.,.]]]]]] => 32

[.,[.,[.,[.,[[.,.],.]]]]] => 32

[.,[.,[.,[[.,.],[.,.]]]]] => 8

[.,[.,[.,[[.,[.,.]],.]]]] => 32

[.,[.,[.,[[[.,.],.],.]]]] => 32

[.,[.,[[.,.],[.,[.,.]]]]] => 16

[.,[.,[[.,.],[[.,.],.]]]] => 16

[.,[.,[[.,[.,.]],[.,.]]]] => 16

[.,[.,[[[.,.],.],[.,.]]]] => 16

[.,[.,[[.,[.,[.,.]]],.]]] => 32

[.,[.,[[.,[[.,.],.]],.]]] => 32

[.,[.,[[[.,.],[.,.]],.]]] => 8

[.,[.,[[[.,[.,.]],.],.]]] => 32

[.,[.,[[[[.,.],.],.],.]]] => 32

[.,[[.,.],[.,[.,[.,.]]]]] => 16

[.,[[.,.],[.,[[.,.],.]]]] => 16

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

[.,[[.,.],[[.,[.,.]],.]]] => 16

[.,[[.,.],[[[.,.],.],.]]] => 16

[.,[[.,[.,.]],[.,[.,.]]]] => 8

[.,[[.,[.,.]],[[.,.],.]]] => 8

[.,[[[.,.],.],[.,[.,.]]]] => 8

[.,[[[.,.],.],[[.,.],.]]] => 8

[.,[[.,[.,[.,.]]],[.,.]]] => 16

[.,[[.,[[.,.],.]],[.,.]]] => 16

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

[.,[[[.,[.,.]],.],[.,.]]] => 16

[.,[[[[.,.],.],.],[.,.]]] => 16

[.,[[.,[.,[.,[.,.]]]],.]] => 32

[.,[[.,[.,[[.,.],.]]],.]] => 32

[.,[[.,[[.,.],[.,.]]],.]] => 8

[.,[[.,[[.,[.,.]],.]],.]] => 32

[.,[[.,[[[.,.],.],.]],.]] => 32

[.,[[[.,.],[.,[.,.]]],.]] => 16

[.,[[[.,.],[[.,.],.]],.]] => 16

[.,[[[.,[.,.]],[.,.]],.]] => 16

[.,[[[[.,.],.],[.,.]],.]] => 16

[.,[[[.,[.,[.,.]]],.],.]] => 32

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Description

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):
    return Binary_to_Rooted(tree.node_number()).count(RootedTree(tree))

Created

Feb 25, 2016 at 10:48 by Martin Rubey

Updated

Feb 25, 2016 at 10:48 by Martin Rubey