Identifier
-
Mp00049:
Ordered trees
—to binary tree: left brother = left child⟶
Binary trees
Mp00009: Binary trees —left rotate⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
St001879: Posets ⟶ ℤ
Values
[[],[],[]] => [[[.,.],.],.] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => 2
[[],[[]]] => [[.,.],[.,.]] => [[[.,.],.],.] => ([(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),(2,1),(3,2)],4) => 3
[[[]],[],[]] => [[[.,[.,.]],.],.] => [.,[[.,[.,.]],.]] => ([(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),(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),(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),(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),(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),(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
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[],[],[],[],[],[],[]] => [[[[[[[.,.],.],.],.],.],.],.] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[],[],[],[],[],[[]]] => [[[[[[.,.],.],.],.],.],[.,.]] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[]],[],[],[],[],[]] => [[[[[[.,[.,.]],.],.],.],.],.] => [.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[]],[],[],[],[[]]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[]],[],[],[],[]] => [[[[[.,[[.,.],.]],.],.],.],.] => [.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]]],[],[],[],[]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[]],[],[],[[]]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]]],[],[],[[]]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[],[]],[],[],[]] => [[[[.,[[[.,.],.],.]],.],.],.] => [.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]],[]],[],[],[]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[]]],[],[],[]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]]]],[],[],[]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[],[]],[],[[]]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]],[]],[],[[]]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[]]],[],[[]]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]]]],[],[[]]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[],[],[]],[],[]] => [[[.,[[[[.,.],.],.],.]],.],.] => [.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]],[],[]],[],[]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[]],[]],[],[]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]]],[]],[],[]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[],[]]],[],[]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]],[]]],[],[]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[],[]]]],[],[]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[[]]]]],[],[]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[],[],[]],[[]]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [[[.,[[[[.,.],.],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]],[],[]],[[]]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [[[.,[[[.,[.,.]],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[]],[]],[[]]] => [[.,[[.,[[.,.],.]],.]],[.,.]] => [[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]]],[]],[[]]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[],[]]],[[]]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [[[.,[.,[[[.,.],.],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]],[]]],[[]]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[],[]]]],[[]]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[[]]]]],[[]]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[],[],[],[],[]],[]] => [[.,[[[[[.,.],.],.],.],.]],.] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[]],[],[],[]],[]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[]],[],[]],[]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]]],[],[]],[]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[],[]],[]],[]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[]],[]],[]],[]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[],[]]],[]],[]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[[[]]]],[]],[]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
[[[[],[],[],[]]],[]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 6
>>> Load all 124 entries. <<<
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
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
left rotate
Description
Return the result of left rotation applied to a binary tree.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
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