- FindStat

Identifier

Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000700: Ordered trees ⟶ ℤ

Values

[.,.] => [[],[]] => 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

>>> Load all 196 entries. <<<

search for individual values

searching the database for the individual values of this statistic

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searching the database for statistics with the same generating function

click to show known generating functions

$F_{1} = q$

$F_{2} = 2\ q$

$F_{3} = 4\ q + q^{2}$

$F_{4} = 10\ q + 4\ q^{2}$

$F_{5} = 28\ q + 14\ q^{2}$

$F_{6} = 84\ q + 48\ q^{2}$

Description

The protection number of an ordered tree.
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.