Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000399
(load all 3 compositions to match this statistic)
Mapping
St000399: Binary trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[.,.]
 => 2
[.,[.,.]]
 => 5
[[.,.],.]
 => 5
[.,[.,[.,.]]]
 => 9
[.,[[.,.],.]]
 => 9
[[.,.],[.,.]]
 => 8
[[.,[.,.]],.]
 => 9
[[[.,.],.],.]
 => 9
[.,[.,[.,[.,.]]]]
 => 14
[.,[.,[[.,.],.]]]
 => 14
[.,[[.,.],[.,.]]]
 => 13
[.,[[.,[.,.]],.]]
 => 14
[.,[[[.,.],.],.]]
 => 14
[[.,.],[.,[.,.]]]
 => 12
[[.,.],[[.,.],.]]
 => 12
[[.,[.,.]],[.,.]]
 => 12
[[[.,.],.],[.,.]]
 => 12
[[.,[.,[.,.]]],.]
 => 14
[[.,[[.,.],.]],.]
 => 14
[[[.,.],[.,.]],.]
 => 13
[[[.,[.,.]],.],.]
 => 14
[[[[.,.],.],.],.]
 => 14
[.,[.,[.,[.,[.,.]]]]]
 => 20
[.,[.,[.,[[.,.],.]]]]
 => 20
[.,[.,[[.,.],[.,.]]]]
 => 19
[.,[.,[[.,[.,.]],.]]]
 => 20
[.,[.,[[[.,.],.],.]]]
 => 20
[.,[[.,.],[.,[.,.]]]]
 => 18
[.,[[.,.],[[.,.],.]]]
 => 18
[.,[[.,[.,.]],[.,.]]]
 => 18
[.,[[[.,.],.],[.,.]]]
 => 18
[.,[[.,[.,[.,.]]],.]]
 => 20
[.,[[.,[[.,.],.]],.]]
 => 20
[.,[[[.,.],[.,.]],.]]
 => 19
[.,[[[.,[.,.]],.],.]]
 => 20
[.,[[[[.,.],.],.],.]]
 => 20
[[.,.],[.,[.,[.,.]]]]
 => 17
[[.,.],[.,[[.,.],.]]]
 => 17
[[.,.],[[.,.],[.,.]]]
 => 16
[[.,.],[[.,[.,.]],.]]
 => 17
[[.,.],[[[.,.],.],.]]
 => 17
[[.,[.,.]],[.,[.,.]]]
 => 16
[[.,[.,.]],[[.,.],.]]
 => 16
[[[.,.],.],[.,[.,.]]]
 => 16
[[[.,.],.],[[.,.],.]]
 => 16
[[.,[.,[.,.]]],[.,.]]
 => 17
[[.,[[.,.],.]],[.,.]]
 => 17
[[[.,.],[.,.]],[.,.]]
 => 16
[[[.,[.,.]],.],[.,.]]
 => 17
[[[[.,.],.],.],[.,.]]
 => 17
Description
The external path length of a binary tree. This is the sum of the lengths of all paths from the root to an external node, see Section 2.3.4.5 of [1]. This is also called the Sackin balance index of a rooted binary tree, see [2].