Identifier
Values
[1] => [1] => ([],1) => ([],1) => 0
[1,2] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 1
[2,1] => [1,2] => ([(0,1)],2) => ([(0,1)],2) => 1
[1,2,3] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
[1,3,2] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
[2,1,3] => [3,2,1] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(1,2)],3) => 1
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
[3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => ([(0,2),(0,3),(1,2),(1,3)],4) => 1
[1,2,3,4] => [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) => 2
[1,2,4,3] => [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) => 2
[1,3,2,4] => [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) => 2
[1,3,4,2] => [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) => 2
[1,4,3,2] => [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) => 1
[2,1,3,4] => [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) => 2
[2,1,4,3] => [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) => 2
[2,3,1,4] => [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) => 2
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[2,4,1,3] => [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) => 2
[2,4,3,1] => [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) => 2
[3,1,2,4] => [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) => 2
[3,1,4,2] => [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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(1,2),(2,3)],4) => 1
[3,2,4,1] => [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) => 2
[3,4,1,2] => [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) => 2
[3,4,2,1] => [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) => 2
[4,1,2,3] => [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) => 1
[4,2,1,3] => [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) => 2
[4,2,3,1] => [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) => 2
[4,3,1,2] => [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) => ([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => 2
[4,3,2,1] => [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) => 2
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(1,3),(2,3),(2,4)],5) => 2
[2,3,4,5,6,1] => [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) => 2
[5,4,3,2,1,6] => [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) => 2
[2,3,4,5,6,7,1] => [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) => 2
[6,5,4,3,2,1,7] => [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) => 2
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 induced matching number of a graph.
An induced matching of a graph is a set of independent edges which is an induced subgraph. This statistic records the maximal number of edges in an induced matching.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
Map
Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $\pi^{-1}c$ where $c = (1,\ldots,n)$ is the long cycle.
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.