Identifier
-
Mp00008:
Binary trees
—to complete tree⟶
Ordered trees
St000166: Ordered trees ⟶ ℤ (values match St000094The depth of an ordered tree.)
Values
[.,.] => [[],[]] => 1
[.,[.,.]] => [[],[[],[]]] => 2
[[.,.],.] => [[[],[]],[]] => 2
[.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[.,[[.,.],.]] => [[],[[[],[]],[]]] => 3
[[.,.],[.,.]] => [[[],[]],[[],[]]] => 2
[[.,[.,.]],.] => [[[],[[],[]]],[]] => 3
[[[.,.],.],.] => [[[[],[]],[]],[]] => 3
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Description
The depth minus 1 of an ordered tree.
The ordered trees of size $n$ are bijection with the Dyck paths of size $n-1$, and this statistic then corresponds to St000013The height of a Dyck path..
The ordered trees of size $n$ are bijection with the Dyck paths of size $n-1$, and this statistic then corresponds to St000013The height of a Dyck path..
Map
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Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
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