Identifier
Values
[1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => 3
[3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => 3
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 3
[5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => 3
[1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,6,5,4,3,2,1] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => ([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
search for individual values
searching the database for the individual values of this statistic
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Map
complement
Description
The complement of a graph.
The complement of a graph has the same vertices, but exactly those edges that are not in the original graph.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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.