Identifier
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] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 3
[-,3,2] => [1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 3
[2,1,+] => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 4
[2,1,-] => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 4
[2,3,1] => [2,3,1] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 4
[3,1,2] => [3,1,2] => [[.,[.,.]],.] => [[[],[[],[]]],[]] => 3
[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] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 4
[-,+,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 4
[+,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 4
[-,-,4,3] => [1,2,4,3] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 4
[+,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] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 3
[-,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 3
[+,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 3
[-,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 3
[+,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 3
[-,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 3
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 length of the boundary minus the length of the trunk of an ordered tree.
This is the size of the set of edges which are either on the left most path or on the right most path from the root.
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.