Identifier
Values
[+] => [1] => ([],1) => 1
[-] => [1] => ([],1) => 1
[+,+] => [1,2] => ([(0,1)],2) => 1
[-,+] => [1,2] => ([(0,1)],2) => 1
[+,-] => [1,2] => ([(0,1)],2) => 1
[-,-] => [1,2] => ([(0,1)],2) => 1
[2,1] => [2,1] => ([(0,1)],2) => 1
[+,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[-,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,1,+] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,1,-] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[3,+,1] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[3,-,1] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[+,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,+,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,-,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
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 connected components of the Hasse diagram for the poset.
Map
permutation
Description
The underlying permutation of the decorated permutation.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.