edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
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[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>6 [[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>6 [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>5 [[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>5 [[.,.],[.,[[.,.],[[.,.],[.,.]]]]]=>3 [[.,.],[.,[[.,.],[[.,[.,.]],.]]]]=>5 [[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>5 [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>4 [[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>4 [[.,.],[.,[[[.,.],.],[.,[.,.]]]]]=>4 [[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>4 [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]=>5 [[.,.],[.,[[.,[[.,.],.]],[.,.]]]]=>5 [[.,.],[.,[[[.,.],[.,.]],[.,.]]]]=>3 [[.,.],[.,[[[.,[.,.]],.],[.,.]]]]=>5 [[.,.],[.,[[[[.,.],.],.],[.,.]]]]=>5 [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>6 [[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>6 [[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>4 [[.,.],[.,[[.,[[.,[.,.]],.]],.]]]=>6 [[.,.],[.,[[.,[[[.,.],.],.]],.]]]=>6 [[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>5 [[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>5 [[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>5 [[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>5 [[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>6 [[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>6 [[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>4 [[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>6 [[.,.],[.,[[[[[.,.],.],.],.],.]]]=>6 [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>5 [[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>5 [[.,.],[[.,.],[.,[[.,.],[.,.]]]]]=>3 [[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>5 [[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>5 [[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>4 [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>4 [[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>4 [[.,.],[[.,.],[[[.,.],.],[.,.]]]]=>4 [[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>5 [[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>5 [[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>3 [[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>5 [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>5 [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>5 [[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>5 [[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>3 [[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>5 [[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>5 [[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>5 [[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>5 [[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>3 [[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>5 [[.,.],[[[.,.],.],[[[.,.],.],.]]]=>5 [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>5 [[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>5 [[.,.],[[.,[[.,.],.]],[.,[.,.]]]]=>5 [[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>5 [[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>3 [[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>3 [[.,.],[[[.,[.,.]],.],[.,[.,.]]]]=>5 [[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>5 [[.,.],[[[[.,.],.],.],[.,[.,.]]]]=>5 [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>5 [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>5 [[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>5 [[.,.],[[.,[[.,.],[.,.]]],[.,.]]]=>3 [[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>5 [[.,.],[[.,[[[.,.],.],.]],[.,.]]]=>5 [[.,.],[[[.,.],[.,[.,.]]],[.,.]]]=>4 [[.,.],[[[.,.],[[.,.],.]],[.,.]]]=>4 [[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>4 [[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>4 [[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>5 [[.,.],[[[.,[[.,.],.]],.],[.,.]]]=>5 [[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>3 [[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>5 [[.,.],[[[[[.,.],.],.],.],[.,.]]]=>5 [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>6 [[.,.],[[.,[.,[.,[[.,.],.]]]],.]]=>6 [[.,.],[[.,[.,[[.,.],[.,.]]]],.]]=>4 [[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>6 [[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>6 [[.,.],[[.,[[.,.],[.,[.,.]]]],.]]=>5 [[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>5 [[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>5 [[.,.],[[.,[[[.,.],.],[.,.]]],.]]=>5 [[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>6 [[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>6 [[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>4 [[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>6 [[.,.],[[.,[[[[.,.],.],.],.]],.]]=>6 [[.,.],[[[.,.],[.,[.,[.,.]]]],.]]=>5 [[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>5 [[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>3 [[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>5 [[.,.],[[[.,.],[[[.,.],.],.]],.]]=>5 [[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>4 [[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>4 [[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>4 [[.,.],[[[[.,.],.],[[.,.],.]],.]]=>4 [[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>5 [[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>5 [[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>3 [[.,.],[[[[.,[.,.]],.],[.,.]],.]]=>5 [[.,.],[[[[[.,.],.],.],[.,.]],.]]=>5 [[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>6 [[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>6 [[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>4 [[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>6 [[.,.],[[[.,[[[.,.],.],.]],.],.]]=>6 [[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>5 [[.,.],[[[[.,.],[[.,.],.]],.],.]]=>5 [[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>5 [[.,.],[[[[[.,.],.],[.,.]],.],.]]=>5 [[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>6 [[.,.],[[[[.,[[.,.],.]],.],.],.]]=>6 [[.,.],[[[[[.,.],[.,.]],.],.],.]]=>4 [[.,.],[[[[[.,[.,.]],.],.],.],.]]=>6 [[.,.],[[[[[[.,.],.],.],.],.],.]]=>6 [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>6 [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>6 [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>4 [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>6 [[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>6 [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]=>5 [[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>5 [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>5 [[.,[.,.]],[.,[[[.,.],.],[.,.]]]]=>5 [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>6 [[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>6 [[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>4 [[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>6 [[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>6 [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>5
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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