edit this statistic or download as text // json
Identifier
Values
=>
Cc0010;cc-rep
[.,[.,.]]=>2 [[.,.],.]=>1 [.,[.,[.,.]]]=>5 [.,[[.,.],.]]=>3 [[.,.],[.,.]]=>2 [[.,[.,.]],.]=>2 [[[.,.],.],.]=>1 [.,[.,[.,[.,.]]]]=>14 [.,[.,[[.,.],.]]]=>9 [.,[[.,.],[.,.]]]=>7 [.,[[.,[.,.]],.]]=>7 [.,[[[.,.],.],.]]=>4 [[.,.],[.,[.,.]]]=>5 [[.,.],[[.,.],.]]=>3 [[.,[.,.]],[.,.]]=>4 [[[.,.],.],[.,.]]=>2 [[.,[.,[.,.]]],.]=>5 [[.,[[.,.],.]],.]=>3 [[[.,.],[.,.]],.]=>2 [[[.,[.,.]],.],.]=>2 [[[[.,.],.],.],.]=>1 [.,[.,[.,[.,[.,.]]]]]=>42 [.,[.,[.,[[.,.],.]]]]=>28 [.,[.,[[.,.],[.,.]]]]=>23 [.,[.,[[.,[.,.]],.]]]=>23 [.,[.,[[[.,.],.],.]]]=>14 [.,[[.,.],[.,[.,.]]]]=>19 [.,[[.,.],[[.,.],.]]]=>12 [.,[[.,[.,.]],[.,.]]]=>16 [.,[[[.,.],.],[.,.]]]=>9 [.,[[.,[.,[.,.]]],.]]=>19 [.,[[.,[[.,.],.]],.]]=>12 [.,[[[.,.],[.,.]],.]]=>9 [.,[[[.,[.,.]],.],.]]=>9 [.,[[[[.,.],.],.],.]]=>5 [[.,.],[.,[.,[.,.]]]]=>14 [[.,.],[.,[[.,.],.]]]=>9 [[.,.],[[.,.],[.,.]]]=>7 [[.,.],[[.,[.,.]],.]]=>7 [[.,.],[[[.,.],.],.]]=>4 [[.,[.,.]],[.,[.,.]]]=>10 [[.,[.,.]],[[.,.],.]]=>6 [[[.,.],.],[.,[.,.]]]=>5 [[[.,.],.],[[.,.],.]]=>3 [[.,[.,[.,.]]],[.,.]]=>10 [[.,[[.,.],.]],[.,.]]=>6 [[[.,.],[.,.]],[.,.]]=>4 [[[.,[.,.]],.],[.,.]]=>4 [[[[.,.],.],.],[.,.]]=>2 [[.,[.,[.,[.,.]]]],.]=>14 [[.,[.,[[.,.],.]]],.]=>9 [[.,[[.,.],[.,.]]],.]=>7 [[.,[[.,[.,.]],.]],.]=>7 [[.,[[[.,.],.],.]],.]=>4 [[[.,.],[.,[.,.]]],.]=>5 [[[.,.],[[.,.],.]],.]=>3 [[[.,[.,.]],[.,.]],.]=>4 [[[[.,.],.],[.,.]],.]=>2 [[[.,[.,[.,.]]],.],.]=>5 [[[.,[[.,.],.]],.],.]=>3 [[[[.,.],[.,.]],.],.]=>2 [[[[.,[.,.]],.],.],.]=>2 [[[[[.,.],.],.],.],.]=>1 [.,[.,[.,[.,[.,[.,.]]]]]]=>132 [.,[.,[.,[.,[[.,.],.]]]]]=>90 [.,[.,[.,[[.,.],[.,.]]]]]=>76 [.,[.,[.,[[.,[.,.]],.]]]]=>76 [.,[.,[.,[[[.,.],.],.]]]]=>48 [.,[.,[[.,.],[.,[.,.]]]]]=>66 [.,[.,[[.,.],[[.,.],.]]]]=>43 [.,[.,[[.,[.,.]],[.,.]]]]=>57 [.,[.,[[[.,.],.],[.,.]]]]=>34 [.,[.,[[.,[.,[.,.]]],.]]]=>66 [.,[.,[[.,[[.,.],.]],.]]]=>43 [.,[.,[[[.,.],[.,.]],.]]]=>34 [.,[.,[[[.,[.,.]],.],.]]]=>34 [.,[.,[[[[.,.],.],.],.]]]=>20 [.,[[.,.],[.,[.,[.,.]]]]]=>56 [.,[[.,.],[.,[[.,.],.]]]]=>37 [.,[[.,.],[[.,.],[.,.]]]]=>30 [.,[[.,.],[[.,[.,.]],.]]]=>30 [.,[[.,.],[[[.,.],.],.]]]=>18 [.,[[.,[.,.]],[.,[.,.]]]]=>43 [.,[[.,[.,.]],[[.,.],.]]]=>27 [.,[[[.,.],.],[.,[.,.]]]]=>24 [.,[[[.,.],.],[[.,.],.]]]=>15 [.,[[.,[.,[.,.]]],[.,.]]]=>43 [.,[[.,[[.,.],.]],[.,.]]]=>27 [.,[[[.,.],[.,.]],[.,.]]]=>20 [.,[[[.,[.,.]],.],[.,.]]]=>20 [.,[[[[.,.],.],.],[.,.]]]=>11 [.,[[.,[.,[.,[.,.]]]],.]]=>56 [.,[[.,[.,[[.,.],.]]],.]]=>37 [.,[[.,[[.,.],[.,.]]],.]]=>30 [.,[[.,[[.,[.,.]],.]],.]]=>30 [.,[[.,[[[.,.],.],.]],.]]=>18 [.,[[[.,.],[.,[.,.]]],.]]=>24 [.,[[[.,.],[[.,.],.]],.]]=>15 [.,[[[.,[.,.]],[.,.]],.]]=>20 [.,[[[[.,.],.],[.,.]],.]]=>11 [.,[[[.,[.,[.,.]]],.],.]]=>24 [.,[[[.,[[.,.],.]],.],.]]=>15 [.,[[[[.,.],[.,.]],.],.]]=>11 [.,[[[[.,[.,.]],.],.],.]]=>11 [.,[[[[[.,.],.],.],.],.]]=>6 [[.,.],[.,[.,[.,[.,.]]]]]=>42 [[.,.],[.,[.,[[.,.],.]]]]=>28 [[.,.],[.,[[.,.],[.,.]]]]=>23 [[.,.],[.,[[.,[.,.]],.]]]=>23 [[.,.],[.,[[[.,.],.],.]]]=>14 [[.,.],[[.,.],[.,[.,.]]]]=>19 [[.,.],[[.,.],[[.,.],.]]]=>12 [[.,.],[[.,[.,.]],[.,.]]]=>16 [[.,.],[[[.,.],.],[.,.]]]=>9 [[.,.],[[.,[.,[.,.]]],.]]=>19 [[.,.],[[.,[[.,.],.]],.]]=>12 [[.,.],[[[.,.],[.,.]],.]]=>9 [[.,.],[[[.,[.,.]],.],.]]=>9 [[.,.],[[[[.,.],.],.],.]]=>5 [[.,[.,.]],[.,[.,[.,.]]]]=>28 [[.,[.,.]],[.,[[.,.],.]]]=>18 [[.,[.,.]],[[.,.],[.,.]]]=>14 [[.,[.,.]],[[.,[.,.]],.]]=>14 [[.,[.,.]],[[[.,.],.],.]]=>8 [[[.,.],.],[.,[.,[.,.]]]]=>14 [[[.,.],.],[.,[[.,.],.]]]=>9 [[[.,.],.],[[.,.],[.,.]]]=>7 [[[.,.],.],[[.,[.,.]],.]]=>7 [[[.,.],.],[[[.,.],.],.]]=>4 [[.,[.,[.,.]]],[.,[.,.]]]=>25 [[.,[.,[.,.]]],[[.,.],.]]=>15 [[.,[[.,.],.]],[.,[.,.]]]=>15 [[.,[[.,.],.]],[[.,.],.]]=>9 [[[.,.],[.,.]],[.,[.,.]]]=>10 [[[.,.],[.,.]],[[.,.],.]]=>6 [[[.,[.,.]],.],[.,[.,.]]]=>10 [[[.,[.,.]],.],[[.,.],.]]=>6 [[[[.,.],.],.],[.,[.,.]]]=>5 [[[[.,.],.],.],[[.,.],.]]=>3 [[.,[.,[.,[.,.]]]],[.,.]]=>28 [[.,[.,[[.,.],.]]],[.,.]]=>18 [[.,[[.,.],[.,.]]],[.,.]]=>14 [[.,[[.,[.,.]],.]],[.,.]]=>14 [[.,[[[.,.],.],.]],[.,.]]=>8 [[[.,.],[.,[.,.]]],[.,.]]=>10 [[[.,.],[[.,.],.]],[.,.]]=>6 [[[.,[.,.]],[.,.]],[.,.]]=>8 [[[[.,.],.],[.,.]],[.,.]]=>4 [[[.,[.,[.,.]]],.],[.,.]]=>10 [[[.,[[.,.],.]],.],[.,.]]=>6 [[[[.,.],[.,.]],.],[.,.]]=>4 [[[[.,[.,.]],.],.],[.,.]]=>4 [[[[[.,.],.],.],.],[.,.]]=>2 [[.,[.,[.,[.,[.,.]]]]],.]=>42 [[.,[.,[.,[[.,.],.]]]],.]=>28 [[.,[.,[[.,.],[.,.]]]],.]=>23 [[.,[.,[[.,[.,.]],.]]],.]=>23 [[.,[.,[[[.,.],.],.]]],.]=>14 [[.,[[.,.],[.,[.,.]]]],.]=>19 [[.,[[.,.],[[.,.],.]]],.]=>12 [[.,[[.,[.,.]],[.,.]]],.]=>16 [[.,[[[.,.],.],[.,.]]],.]=>9 [[.,[[.,[.,[.,.]]],.]],.]=>19 [[.,[[.,[[.,.],.]],.]],.]=>12 [[.,[[[.,.],[.,.]],.]],.]=>9 [[.,[[[.,[.,.]],.],.]],.]=>9 [[.,[[[[.,.],.],.],.]],.]=>5 [[[.,.],[.,[.,[.,.]]]],.]=>14 [[[.,.],[.,[[.,.],.]]],.]=>9 [[[.,.],[[.,.],[.,.]]],.]=>7 [[[.,.],[[.,[.,.]],.]],.]=>7 [[[.,.],[[[.,.],.],.]],.]=>4 [[[.,[.,.]],[.,[.,.]]],.]=>10 [[[.,[.,.]],[[.,.],.]],.]=>6 [[[[.,.],.],[.,[.,.]]],.]=>5 [[[[.,.],.],[[.,.],.]],.]=>3 [[[.,[.,[.,.]]],[.,.]],.]=>10 [[[.,[[.,.],.]],[.,.]],.]=>6 [[[[.,.],[.,.]],[.,.]],.]=>4 [[[[.,[.,.]],.],[.,.]],.]=>4 [[[[[.,.],.],.],[.,.]],.]=>2 [[[.,[.,[.,[.,.]]]],.],.]=>14 [[[.,[.,[[.,.],.]]],.],.]=>9 [[[.,[[.,.],[.,.]]],.],.]=>7 [[[.,[[.,[.,.]],.]],.],.]=>7 [[[.,[[[.,.],.],.]],.],.]=>4 [[[[.,.],[.,[.,.]]],.],.]=>5 [[[[.,.],[[.,.],.]],.],.]=>3 [[[[.,[.,.]],[.,.]],.],.]=>4 [[[[[.,.],.],[.,.]],.],.]=>2 [[[[.,[.,[.,.]]],.],.],.]=>5 [[[[.,[[.,.],.]],.],.],.]=>3 [[[[[.,.],[.,.]],.],.],.]=>2 [[[[[.,[.,.]],.],.],.],.]=>2 [[[[[[.,.],.],.],.],.],.]=>1
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 elements smaller than a binary tree in Tamari order.
References
[1] Chatel, Grégory, Pons, V. Counting smaller trees in the Tamari order MathSciNet:3091011
Code
def statistic(tree):
    return len(tree.tamari_smaller())
Created
Jun 13, 2013 at 09:55 by Viviane Pons
Updated
Oct 17, 2015 at 10:48 by Christian Stump