Identifier
-
Mp00253:
Decorated permutations
—permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000521: Ordered trees ⟶ ℤ
Values
[+] => [1] => [.,.] => [[],[]] => 2
[-] => [1] => [.,.] => [[],[]] => 2
[+,+] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 3
[-,+] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 3
[+,-] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 3
[-,-] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 3
[2,1] => [2,1] => [[.,.],.] => [[[],[]],[]] => 3
[+,+,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[-,+,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[+,-,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[+,+,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[-,-,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[-,+,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[+,-,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[-,-,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 4
[+,3,2] => [1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 4
[-,3,2] => [1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 4
[2,1,+] => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 3
[2,1,-] => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 3
[2,3,1] => [2,3,1] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 3
[3,1,2] => [3,1,2] => [[.,[.,.]],.] => [[[],[[],[]]],[]] => 4
[3,+,1] => [3,2,1] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 4
[3,-,1] => [3,2,1] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 4
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 5
[+,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 5
[-,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 5
[+,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 5
[-,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 5
[+,3,2,+] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
[-,3,2,+] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
[+,3,2,-] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
[-,3,2,-] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
[+,3,4,2] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
[-,3,4,2] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 4
[+,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 5
[-,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 5
[+,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 5
[-,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 5
[+,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 5
[-,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 5
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Description
The number of distinct subtrees of an ordered tree.
A subtree is specified by a node of the tree. Thus, the tree consisting of a single path has as many subtrees as nodes, whereas the tree of height two, having all leaves attached to the root, has only two distinct subtrees. Because we consider ordered trees, the tree $[[[[]], []], [[], [[]]]]$ on nine nodes has five distinct subtrees.
A subtree is specified by a node of the tree. Thus, the tree consisting of a single path has as many subtrees as nodes, whereas the tree of height two, having all leaves attached to the root, has only two distinct subtrees. Because we consider ordered trees, the tree $[[[[]], []], [[], [[]]]]$ on nine nodes has five distinct subtrees.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
Map
permutation
Description
The underlying permutation of the decorated permutation.
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