Identifier
Values
=>
Cc0014;cc-rep-2 Cc0020;cc-rep
[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
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.
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.