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Identifier
Values
=>
Cc0010;cc-rep
[.,[.,.]]=>1 [[.,.],.]=>2 [.,[.,[.,.]]]=>1 [.,[[.,.],.]]=>1 [[.,.],[.,.]]=>2 [[.,[.,.]],.]=>2 [[[.,.],.],.]=>3 [.,[.,[.,[.,.]]]]=>1 [.,[.,[[.,.],.]]]=>1 [.,[[.,.],[.,.]]]=>1 [.,[[.,[.,.]],.]]=>1 [.,[[[.,.],.],.]]=>1 [[.,.],[.,[.,.]]]=>2 [[.,.],[[.,.],.]]=>2 [[.,[.,.]],[.,.]]=>2 [[[.,.],.],[.,.]]=>3 [[.,[.,[.,.]]],.]=>2 [[.,[[.,.],.]],.]=>2 [[[.,.],[.,.]],.]=>3 [[[.,[.,.]],.],.]=>3 [[[[.,.],.],.],.]=>4 [.,[.,[.,[.,[.,.]]]]]=>1 [.,[.,[.,[[.,.],.]]]]=>1 [.,[.,[[.,.],[.,.]]]]=>1 [.,[.,[[.,[.,.]],.]]]=>1 [.,[.,[[[.,.],.],.]]]=>1 [.,[[.,.],[.,[.,.]]]]=>1 [.,[[.,.],[[.,.],.]]]=>1 [.,[[.,[.,.]],[.,.]]]=>1 [.,[[[.,.],.],[.,.]]]=>1 [.,[[.,[.,[.,.]]],.]]=>1 [.,[[.,[[.,.],.]],.]]=>1 [.,[[[.,.],[.,.]],.]]=>1 [.,[[[.,[.,.]],.],.]]=>1 [.,[[[[.,.],.],.],.]]=>1 [[.,.],[.,[.,[.,.]]]]=>2 [[.,.],[.,[[.,.],.]]]=>2 [[.,.],[[.,.],[.,.]]]=>2 [[.,.],[[.,[.,.]],.]]=>2 [[.,.],[[[.,.],.],.]]=>2 [[.,[.,.]],[.,[.,.]]]=>2 [[.,[.,.]],[[.,.],.]]=>2 [[[.,.],.],[.,[.,.]]]=>3 [[[.,.],.],[[.,.],.]]=>3 [[.,[.,[.,.]]],[.,.]]=>2 [[.,[[.,.],.]],[.,.]]=>2 [[[.,.],[.,.]],[.,.]]=>3 [[[.,[.,.]],.],[.,.]]=>3 [[[[.,.],.],.],[.,.]]=>4 [[.,[.,[.,[.,.]]]],.]=>2 [[.,[.,[[.,.],.]]],.]=>2 [[.,[[.,.],[.,.]]],.]=>2 [[.,[[.,[.,.]],.]],.]=>2 [[.,[[[.,.],.],.]],.]=>2 [[[.,.],[.,[.,.]]],.]=>3 [[[.,.],[[.,.],.]],.]=>3 [[[.,[.,.]],[.,.]],.]=>3 [[[[.,.],.],[.,.]],.]=>4 [[[.,[.,[.,.]]],.],.]=>3 [[[.,[[.,.],.]],.],.]=>3 [[[[.,.],[.,.]],.],.]=>4 [[[[.,[.,.]],.],.],.]=>4 [[[[[.,.],.],.],.],.]=>5 [.,[.,[.,[.,[.,[.,.]]]]]]=>1 [.,[.,[.,[.,[[.,.],.]]]]]=>1 [.,[.,[.,[[.,.],[.,.]]]]]=>1 [.,[.,[.,[[.,[.,.]],.]]]]=>1 [.,[.,[.,[[[.,.],.],.]]]]=>1 [.,[.,[[.,.],[.,[.,.]]]]]=>1 [.,[.,[[.,.],[[.,.],.]]]]=>1 [.,[.,[[.,[.,.]],[.,.]]]]=>1 [.,[.,[[[.,.],.],[.,.]]]]=>1 [.,[.,[[.,[.,[.,.]]],.]]]=>1 [.,[.,[[.,[[.,.],.]],.]]]=>1 [.,[.,[[[.,.],[.,.]],.]]]=>1 [.,[.,[[[.,[.,.]],.],.]]]=>1 [.,[.,[[[[.,.],.],.],.]]]=>1 [.,[[.,.],[.,[.,[.,.]]]]]=>1 [.,[[.,.],[.,[[.,.],.]]]]=>1 [.,[[.,.],[[.,.],[.,.]]]]=>1 [.,[[.,.],[[.,[.,.]],.]]]=>1 [.,[[.,.],[[[.,.],.],.]]]=>1 [.,[[.,[.,.]],[.,[.,.]]]]=>1 [.,[[.,[.,.]],[[.,.],.]]]=>1 [.,[[[.,.],.],[.,[.,.]]]]=>1 [.,[[[.,.],.],[[.,.],.]]]=>1 [.,[[.,[.,[.,.]]],[.,.]]]=>1 [.,[[.,[[.,.],.]],[.,.]]]=>1 [.,[[[.,.],[.,.]],[.,.]]]=>1 [.,[[[.,[.,.]],.],[.,.]]]=>1 [.,[[[[.,.],.],.],[.,.]]]=>1 [.,[[.,[.,[.,[.,.]]]],.]]=>1 [.,[[.,[.,[[.,.],.]]],.]]=>1 [.,[[.,[[.,.],[.,.]]],.]]=>1 [.,[[.,[[.,[.,.]],.]],.]]=>1 [.,[[.,[[[.,.],.],.]],.]]=>1 [.,[[[.,.],[.,[.,.]]],.]]=>1 [.,[[[.,.],[[.,.],.]],.]]=>1 [.,[[[.,[.,.]],[.,.]],.]]=>1 [.,[[[[.,.],.],[.,.]],.]]=>1 [.,[[[.,[.,[.,.]]],.],.]]=>1 [.,[[[.,[[.,.],.]],.],.]]=>1 [.,[[[[.,.],[.,.]],.],.]]=>1 [.,[[[[.,[.,.]],.],.],.]]=>1 [.,[[[[[.,.],.],.],.],.]]=>1 [[.,.],[.,[.,[.,[.,.]]]]]=>2 [[.,.],[.,[.,[[.,.],.]]]]=>2 [[.,.],[.,[[.,.],[.,.]]]]=>2 [[.,.],[.,[[.,[.,.]],.]]]=>2 [[.,.],[.,[[[.,.],.],.]]]=>2 [[.,.],[[.,.],[.,[.,.]]]]=>2 [[.,.],[[.,.],[[.,.],.]]]=>2 [[.,.],[[.,[.,.]],[.,.]]]=>2 [[.,.],[[[.,.],.],[.,.]]]=>2 [[.,.],[[.,[.,[.,.]]],.]]=>2 [[.,.],[[.,[[.,.],.]],.]]=>2 [[.,.],[[[.,.],[.,.]],.]]=>2 [[.,.],[[[.,[.,.]],.],.]]=>2 [[.,.],[[[[.,.],.],.],.]]=>2 [[.,[.,.]],[.,[.,[.,.]]]]=>2 [[.,[.,.]],[.,[[.,.],.]]]=>2 [[.,[.,.]],[[.,.],[.,.]]]=>2 [[.,[.,.]],[[.,[.,.]],.]]=>2 [[.,[.,.]],[[[.,.],.],.]]=>2 [[[.,.],.],[.,[.,[.,.]]]]=>3 [[[.,.],.],[.,[[.,.],.]]]=>3 [[[.,.],.],[[.,.],[.,.]]]=>3 [[[.,.],.],[[.,[.,.]],.]]=>3 [[[.,.],.],[[[.,.],.],.]]=>3 [[.,[.,[.,.]]],[.,[.,.]]]=>2 [[.,[.,[.,.]]],[[.,.],.]]=>2 [[.,[[.,.],.]],[.,[.,.]]]=>2 [[.,[[.,.],.]],[[.,.],.]]=>2 [[[.,.],[.,.]],[.,[.,.]]]=>3 [[[.,.],[.,.]],[[.,.],.]]=>3 [[[.,[.,.]],.],[.,[.,.]]]=>3 [[[.,[.,.]],.],[[.,.],.]]=>3 [[[[.,.],.],.],[.,[.,.]]]=>4 [[[[.,.],.],.],[[.,.],.]]=>4 [[.,[.,[.,[.,.]]]],[.,.]]=>2 [[.,[.,[[.,.],.]]],[.,.]]=>2 [[.,[[.,.],[.,.]]],[.,.]]=>2 [[.,[[.,[.,.]],.]],[.,.]]=>2 [[.,[[[.,.],.],.]],[.,.]]=>2 [[[.,.],[.,[.,.]]],[.,.]]=>3 [[[.,.],[[.,.],.]],[.,.]]=>3 [[[.,[.,.]],[.,.]],[.,.]]=>3 [[[[.,.],.],[.,.]],[.,.]]=>4 [[[.,[.,[.,.]]],.],[.,.]]=>3 [[[.,[[.,.],.]],.],[.,.]]=>3 [[[[.,.],[.,.]],.],[.,.]]=>4 [[[[.,[.,.]],.],.],[.,.]]=>4 [[[[[.,.],.],.],.],[.,.]]=>5 [[.,[.,[.,[.,[.,.]]]]],.]=>2 [[.,[.,[.,[[.,.],.]]]],.]=>2 [[.,[.,[[.,.],[.,.]]]],.]=>2 [[.,[.,[[.,[.,.]],.]]],.]=>2 [[.,[.,[[[.,.],.],.]]],.]=>2 [[.,[[.,.],[.,[.,.]]]],.]=>2 [[.,[[.,.],[[.,.],.]]],.]=>2 [[.,[[.,[.,.]],[.,.]]],.]=>2 [[.,[[[.,.],.],[.,.]]],.]=>2 [[.,[[.,[.,[.,.]]],.]],.]=>2 [[.,[[.,[[.,.],.]],.]],.]=>2 [[.,[[[.,.],[.,.]],.]],.]=>2 [[.,[[[.,[.,.]],.],.]],.]=>2 [[.,[[[[.,.],.],.],.]],.]=>2 [[[.,.],[.,[.,[.,.]]]],.]=>3 [[[.,.],[.,[[.,.],.]]],.]=>3 [[[.,.],[[.,.],[.,.]]],.]=>3 [[[.,.],[[.,[.,.]],.]],.]=>3 [[[.,.],[[[.,.],.],.]],.]=>3 [[[.,[.,.]],[.,[.,.]]],.]=>3 [[[.,[.,.]],[[.,.],.]],.]=>3 [[[[.,.],.],[.,[.,.]]],.]=>4 [[[[.,.],.],[[.,.],.]],.]=>4 [[[.,[.,[.,.]]],[.,.]],.]=>3 [[[.,[[.,.],.]],[.,.]],.]=>3 [[[[.,.],[.,.]],[.,.]],.]=>4 [[[[.,[.,.]],.],[.,.]],.]=>4 [[[[[.,.],.],.],[.,.]],.]=>5 [[[.,[.,[.,[.,.]]]],.],.]=>3 [[[.,[.,[[.,.],.]]],.],.]=>3 [[[.,[[.,.],[.,.]]],.],.]=>3 [[[.,[[.,[.,.]],.]],.],.]=>3 [[[.,[[[.,.],.],.]],.],.]=>3 [[[[.,.],[.,[.,.]]],.],.]=>4 [[[[.,.],[[.,.],.]],.],.]=>4 [[[[.,[.,.]],[.,.]],.],.]=>4 [[[[[.,.],.],[.,.]],.],.]=>5 [[[[.,[.,[.,.]]],.],.],.]=>4 [[[[.,[[.,.],.]],.],.],.]=>4 [[[[[.,.],[.,.]],.],.],.]=>5 [[[[[.,[.,.]],.],.],.],.]=>5 [[[[[[.,.],.],.],.],.],.]=>6
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Description
The number of nodes on the left branch of a binary tree.
Also corresponds to ST000011 after applying the Tamari bijection between binary trees and Dyck path.
References
[1] Chapoton, F. Sur le nombre d'intervalles dans les treillis de Tamari MathSciNet:2264942
Code
def statistic(tree):
    if(not tree):
        return 0
    else: return 1 + statistic(tree[0])
Created
Apr 30, 2013 at 11:04 by Viviane Pons
Updated
Oct 17, 2015 at 10:47 by Christian Stump