Identifier
-
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001668: Posets ⟶ ℤ
Values
[[],[]] => [[.,.],.] => ([(0,1)],2) => 1
[[[]]] => [.,[.,.]] => ([(0,1)],2) => 1
[[],[],[]] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => 2
[[],[[]]] => [[.,.],[.,.]] => ([(0,2),(1,2)],3) => 1
[[[]],[]] => [[.,[.,.]],.] => ([(0,2),(2,1)],3) => 2
[[[],[]]] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 2
[[[[]]]] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => 2
[[],[],[],[]] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => 3
[[],[],[[]]] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 2
[[],[[]],[]] => [[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4) => 2
[[],[[],[]]] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => 2
[[],[[[]]]] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => 2
[[[]],[],[]] => [[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => 3
[[[]],[[]]] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 2
[[[],[]],[]] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => 3
[[[[]]],[]] => [[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => 3
[[[],[],[]]] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => 3
[[[],[[]]]] => [.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4) => 2
[[[[]],[]]] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => 3
[[[[],[]]]] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => 3
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => 3
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 3
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 3
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => 3
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 2
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => 2
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 3
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => 3
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => 3
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5) => 3
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5) => 3
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => 3
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => 3
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The number of points of the poset minus the width of the poset.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
searching the database
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