Identifier
-
Mp00008:
Binary trees
—to complete tree⟶
Ordered trees
St000700: Ordered trees ⟶ ℤ
Values
=>
Cc0010;cc-rep-0
Cc0021;cc-rep
[.,.]=>[[],[]]=>1
[.,[.,.]]=>[[],[[],[]]]=>1
[[.,.],.]=>[[[],[]],[]]=>1
[.,[.,[.,.]]]=>[[],[[],[[],[]]]]=>1
[.,[[.,.],.]]=>[[],[[[],[]],[]]]=>1
[[.,.],[.,.]]=>[[[],[]],[[],[]]]=>2
[[.,[.,.]],.]=>[[[],[[],[]]],[]]=>1
[[[.,.],.],.]=>[[[[],[]],[]],[]]=>1
[.,[.,[.,[.,.]]]]=>[[],[[],[[],[[],[]]]]]=>1
[.,[.,[[.,.],.]]]=>[[],[[],[[[],[]],[]]]]=>1
[.,[[.,.],[.,.]]]=>[[],[[[],[]],[[],[]]]]=>1
[.,[[.,[.,.]],.]]=>[[],[[[],[[],[]]],[]]]=>1
[.,[[[.,.],.],.]]=>[[],[[[[],[]],[]],[]]]=>1
[[.,.],[.,[.,.]]]=>[[[],[]],[[],[[],[]]]]=>2
[[.,.],[[.,.],.]]=>[[[],[]],[[[],[]],[]]]=>2
[[.,[.,.]],[.,.]]=>[[[],[[],[]]],[[],[]]]=>2
[[[.,.],.],[.,.]]=>[[[[],[]],[]],[[],[]]]=>2
[[.,[.,[.,.]]],.]=>[[[],[[],[[],[]]]],[]]=>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
[[.,[.,[.,[.,.]]]],.]=>[[[],[[],[[],[[],[]]]]],[]]=>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
[.,[[.,[.,[.,[.,.]]]],.]]=>[[],[[[],[[],[[],[[],[]]]]],[]]]=>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
[[[.,.],.],[.,[.,[.,.]]]]=>[[[[],[]],[]],[[],[[],[[],[]]]]]=>2
[[[.,.],.],[.,[[.,.],.]]]=>[[[[],[]],[]],[[],[[[],[]],[]]]]=>2
[[[.,.],.],[[.,.],[.,.]]]=>[[[[],[]],[]],[[[],[]],[[],[]]]]=>2
[[[.,.],.],[[.,[.,.]],.]]=>[[[[],[]],[]],[[[],[[],[]]],[]]]=>2
[[[.,.],.],[[[.,.],.],.]]=>[[[[],[]],[]],[[[[],[]],[]],[]]]=>2
[[.,[.,[.,.]]],[.,[.,.]]]=>[[[],[[],[[],[]]]],[[],[[],[]]]]=>2
[[.,[.,[.,.]]],[[.,.],.]]=>[[[],[[],[[],[]]]],[[[],[]],[]]]=>2
[[.,[[.,.],.]],[.,[.,.]]]=>[[[],[[[],[]],[]]],[[],[[],[]]]]=>2
[[.,[[.,.],.]],[[.,.],.]]=>[[[],[[[],[]],[]]],[[[],[]],[]]]=>2
[[[.,.],[.,.]],[.,[.,.]]]=>[[[[],[]],[[],[]]],[[],[[],[]]]]=>2
[[[.,.],[.,.]],[[.,.],.]]=>[[[[],[]],[[],[]]],[[[],[]],[]]]=>2
[[[.,[.,.]],.],[.,[.,.]]]=>[[[[],[[],[]]],[]],[[],[[],[]]]]=>2
[[[.,[.,.]],.],[[.,.],.]]=>[[[[],[[],[]]],[]],[[[],[]],[]]]=>2
[[[[.,.],.],.],[.,[.,.]]]=>[[[[[],[]],[]],[]],[[],[[],[]]]]=>2
[[[[.,.],.],.],[[.,.],.]]=>[[[[[],[]],[]],[]],[[[],[]],[]]]=>2
[[.,[.,[.,[.,.]]]],[.,.]]=>[[[],[[],[[],[[],[]]]]],[[],[]]]=>2
[[.,[.,[[.,.],.]]],[.,.]]=>[[[],[[],[[[],[]],[]]]],[[],[]]]=>2
[[.,[[.,.],[.,.]]],[.,.]]=>[[[],[[[],[]],[[],[]]]],[[],[]]]=>2
[[.,[[.,[.,.]],.]],[.,.]]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>2
[[.,[[[.,.],.],.]],[.,.]]=>[[[],[[[[],[]],[]],[]]],[[],[]]]=>2
[[[.,.],[.,[.,.]]],[.,.]]=>[[[[],[]],[[],[[],[]]]],[[],[]]]=>2
[[[.,.],[[.,.],.]],[.,.]]=>[[[[],[]],[[[],[]],[]]],[[],[]]]=>2
[[[.,[.,.]],[.,.]],[.,.]]=>[[[[],[[],[]]],[[],[]]],[[],[]]]=>2
[[[[.,.],.],[.,.]],[.,.]]=>[[[[[],[]],[]],[[],[]]],[[],[]]]=>2
[[[.,[.,[.,.]]],.],[.,.]]=>[[[[],[[],[[],[]]]],[]],[[],[]]]=>2
[[[.,[[.,.],.]],.],[.,.]]=>[[[[],[[[],[]],[]]],[]],[[],[]]]=>2
[[[[.,.],[.,.]],.],[.,.]]=>[[[[[],[]],[[],[]]],[]],[[],[]]]=>2
[[[[.,[.,.]],.],.],[.,.]]=>[[[[[],[[],[]]],[]],[]],[[],[]]]=>2
[[[[[.,.],.],.],.],[.,.]]=>[[[[[[],[]],[]],[]],[]],[[],[]]]=>2
[[.,[.,[.,[.,[.,.]]]]],.]=>[[[],[[],[[],[[],[[],[]]]]]],[]]=>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
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
Description
The protection number of an ordered tree.
This is the minimal distance from the root to a leaf.
This is the minimal distance from the root to a leaf.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
searching the database
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