Identifier
-
Mp00019:
Binary trees
—right rotate⟶
Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
St001645: Graphs ⟶ ℤ
Values
[.,.] => [.,.] => ([],1) => 1
[.,[.,.]] => [[.,.],.] => ([(0,1)],2) => 2
[[.,.],.] => [.,[.,.]] => ([(0,1)],2) => 2
[.,[.,[.,.]]] => [[.,[.,.]],.] => ([(0,2),(1,2)],3) => 4
[.,[[.,.],.]] => [[[.,.],.],.] => ([(0,2),(1,2)],3) => 4
[[.,.],[.,.]] => [.,[.,[.,.]]] => ([(0,2),(1,2)],3) => 4
[[.,[.,.]],.] => [.,[[.,.],.]] => ([(0,2),(1,2)],3) => 4
[[[.,.],.],.] => [[.,.],[.,.]] => ([(0,2),(1,2)],3) => 4
[.,[.,[.,[.,.]]]] => [[.,[.,[.,.]]],.] => ([(0,3),(1,2),(2,3)],4) => 8
[.,[.,[[.,.],.]]] => [[.,[[.,.],.]],.] => ([(0,3),(1,2),(2,3)],4) => 8
[.,[[.,[.,.]],.]] => [[[.,[.,.]],.],.] => ([(0,3),(1,2),(2,3)],4) => 8
[.,[[[.,.],.],.]] => [[[[.,.],.],.],.] => ([(0,3),(1,2),(2,3)],4) => 8
[[.,.],[.,[.,.]]] => [.,[.,[.,[.,.]]]] => ([(0,3),(1,2),(2,3)],4) => 8
[[.,.],[[.,.],.]] => [.,[.,[[.,.],.]]] => ([(0,3),(1,2),(2,3)],4) => 8
[[[.,.],.],[.,.]] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => 8
[[.,[.,[.,.]]],.] => [.,[[.,[.,.]],.]] => ([(0,3),(1,2),(2,3)],4) => 8
[[.,[[.,.],.]],.] => [.,[[[.,.],.],.]] => ([(0,3),(1,2),(2,3)],4) => 8
[[[.,.],[.,.]],.] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => 8
[[[.,[.,.]],.],.] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 8
[[[[.,.],.],.],.] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => 8
[.,[.,[.,[.,[.,.]]]]] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[.,[.,[[.,.],.]]]] => [[.,[.,[[.,.],.]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[.,[[.,[.,.]],.]]] => [[.,[[.,[.,.]],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[.,[[[.,.],.],.]]] => [[.,[[[.,.],.],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[[.,[.,[.,.]]],.]] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[[.,[[.,.],.]],.]] => [[[.,[[.,.],.]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[[[.,[.,.]],.],.]] => [[[[.,[.,.]],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[[[[.,.],.],.],.]] => [[[[[.,.],.],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,.],[.,[.,[.,.]]]] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,.],[.,[[.,.],.]]] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,.],[[.,[.,.]],.]] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,.],[[[.,.],.],.]] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,.],.],[.,[.,.]]] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,.],.],[[.,.],.]] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,[.,.]],.],[.,.]] => [[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[[.,.],.],.],[.,.]] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,[.,[.,[.,.]]]],.] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,[.,[[.,.],.]]],.] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,[[.,[.,.]],.]],.] => [.,[[[.,[.,.]],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[.,[[[.,.],.],.]],.] => [.,[[[[.,.],.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,.],[.,[.,.]]],.] => [[.,.],[[.,[.,.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,.],[[.,.],.]],.] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,[.,.]],[.,.]],.] => [[.,[.,.]],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[[.,.],.],[.,.]],.] => [[[.,.],.],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,[.,[.,.]]],.],.] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[.,[[.,.],.]],.],.] => [[.,[[.,.],.]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[[.,[.,.]],.],.],.] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[[[[[.,.],.],.],.],.] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => 16
[.,[.,[.,[.,[.,[.,.]]]]]] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[.,[.,[[.,.],.]]]]] => [[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[.,[[.,[.,.]],.]]]] => [[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[.,[[[.,.],.],.]]]] => [[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[[.,[.,[.,.]]],.]]] => [[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[[.,[[.,.],.]],.]]] => [[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[[[.,[.,.]],.],.]]] => [[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[.,[[[[.,.],.],.],.]]] => [[.,[[[[.,.],.],.],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[.,[.,[.,[.,.]]]],.]] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[.,[.,[[.,.],.]]],.]] => [[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[.,[[.,[.,.]],.]],.]] => [[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[.,[[[.,.],.],.]],.]] => [[[.,[[[.,.],.],.]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[[.,[.,[.,.]]],.],.]] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[[.,[[.,.],.]],.],.]] => [[[[.,[[.,.],.]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[[[.,[.,.]],.],.],.]] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[.,[[[[[.,.],.],.],.],.]] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[.,[.,[.,[.,.]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[.,[.,[[.,.],.]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[.,[[.,[.,.]],.]]] => [.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[.,[[[.,.],.],.]]] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[[.,[.,[.,.]]],.]] => [.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[[.,[[.,.],.]],.]] => [.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[[[.,[.,.]],.],.]] => [.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,.],[[[[.,.],.],.],.]] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],.],[.,[.,[.,.]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],.],[.,[[.,.],.]]] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],.],[[.,[.,.]],.]] => [[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],.],[[[.,.],.],.]] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[.,.]],.],[.,[.,.]]] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[.,.]],.],[[.,.],.]] => [[.,[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[[.,.],.],.],[.,[.,.]]] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[[.,.],.],.],[[.,.],.]] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[.,[.,.]]],.],[.,.]] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[[.,.],.]],.],[.,.]] => [[.,[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[[.,[.,.]],.],.],[.,.]] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[[[.,.],.],.],.],[.,.]] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[.,[.,[.,[.,.]]]]],.] => [.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[.,[.,[[.,.],.]]]],.] => [.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[.,[[.,[.,.]],.]]],.] => [.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[.,[[[.,.],.],.]]],.] => [.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[[.,[.,[.,.]]],.]],.] => [.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[[.,[[.,.],.]],.]],.] => [.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[[[.,[.,.]],.],.]],.] => [.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[.,[[[[.,.],.],.],.]],.] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],[.,[.,[.,.]]]],.] => [[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],[.,[[.,.],.]]],.] => [[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],[[.,[.,.]],.]],.] => [[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,.],[[[.,.],.],.]],.] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[.,.]],[.,[.,.]]],.] => [[.,[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[.,.]],[[.,.],.]],.] => [[.,[.,.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[[.,.],.],[.,[.,.]]],.] => [[[.,.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[[.,.],.],[[.,.],.]],.] => [[[.,.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
[[[.,[.,[.,.]]],[.,.]],.] => [[.,[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 32
>>> Load all 256 entries. <<<
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 pebbling number of a connected graph.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
Map
right rotate
Description
Return the result of right rotation applied to a binary tree.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!