Identifier
Values
[+] => [1] => [.,.] => [[],[]] => 1
[-] => [1] => [.,.] => [[],[]] => 1
[+,+] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 2
[-,+] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 2
[+,-] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 2
[-,-] => [1,2] => [.,[.,.]] => [[],[[],[]]] => 2
[2,1] => [2,1] => [[.,.],.] => [[[],[]],[]] => 2
[+,+,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[-,+,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[+,-,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[+,+,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[-,-,+] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[-,+,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[+,-,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[-,-,-] => [1,2,3] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 3
[+,3,2] => [1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 3
[-,3,2] => [1,3,2] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 3
[2,1,+] => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 2
[2,1,-] => [2,1,3] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 2
[2,3,1] => [2,3,1] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 2
[3,1,2] => [3,1,2] => [[.,[.,.]],.] => [[[],[[],[]]],[]] => 3
[3,+,1] => [3,2,1] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 3
[3,-,1] => [3,2,1] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 3
[+,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,+,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,-,+,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,+,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,+,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,-,-,+] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,-,+,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,+,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[-,-,-,-] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 4
[+,+,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] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3
[-,3,2,+] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3
[+,3,2,-] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3
[-,3,2,-] => [1,3,2,4] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3
[+,3,4,2] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3
[-,3,4,2] => [1,3,4,2] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3
[+,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 4
[-,4,2,3] => [1,4,2,3] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 4
[+,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 4
[-,4,+,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 4
[+,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 4
[-,4,-,2] => [1,4,3,2] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 4
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 number of 1-protected nodes of a rooted tree.
This is the number of nodes with minimal distance one to a leaf.
Map
permutation
Description
The underlying permutation of the decorated permutation.
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.