edit this statistic or download as text // json
Identifier
Values
[.,[.,.]] => 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
>>> Load all 195 entries. <<<
[.,[[[.,[[.,.],.]],.],.]] => 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
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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