Identifier
Mp00058: Perfect matchings to permutationPermutations
Mp00086: Permutations first fundamental transformationPermutations
Mp00108: Permutations cycle type Integer partitions
Images
=>
Cc0012;cc-rep-0Cc0002;cc-rep-3
[(1,2)]=>[2,1]=>[2,1]=>[2] [(1,2),(3,4)]=>[2,1,4,3]=>[2,1,4,3]=>[2,2] [(1,3),(2,4)]=>[3,4,1,2]=>[2,4,3,1]=>[3,1] [(1,4),(2,3)]=>[4,3,2,1]=>[4,1,2,3]=>[4] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,2,2] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>[3,2,1] [(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>[4,2] [(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[4,5,2,6,3,1]=>[3,3] [(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[6,5,2,1,4,3]=>[6] [(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[6,3,1,5,2,4]=>[6] [(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[3,1,6,5,4,2]=>[4,2] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[4,1,1] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>[3,2,1] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>[3,2,1] [(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>[4,2] [(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[5,6,3,2,4,1]=>[5,1] [(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[3,6,2,4,1,5]=>[5,1] [(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[2,6,1,3,5,4]=>[5,1] [(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[6] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,2,2,2] [(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[4,1,2,3,8,5,6,7]=>[4,4]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
cycle type
Description
The cycle type of a permutation as a partition.