Identifier
Values
[1] => ([],1) => ([],1) => 0
[1,2] => ([(0,1)],2) => ([],2) => 0
[2,1] => ([(0,1)],2) => ([],2) => 0
[1,2,3] => ([(0,2),(2,1)],3) => ([],3) => 0
[1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(2,3)],4) => 1
[3,2,1] => ([(0,2),(2,1)],3) => ([],3) => 0
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
[2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(2,5),(3,4)],6) => 2
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => ([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 2
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(2,5),(3,4),(4,5)],6) => 2
[4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => ([],4) => 0
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([],5) => 0
[1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([],6) => 0
[1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 0
[7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([],7) => 0
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 positive eigenvalues of the adjacency matrix of the graph.
Map
incomparability graph
Description
The incomparability graph of a poset.
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.