- FindStat

Identifier

Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00223: Permutations —runsort⟶ Permutations

Images

=>
            
              Cc0012;cc-rep-0
            

            [(1,2)]=>[2,1]=>[1,2]=>[1,2]
[(1,2),(3,4)]=>[2,1,4,3]=>[1,2,3,4]=>[1,2,3,4]
[(1,3),(2,4)]=>[3,4,1,2]=>[1,3,2,4]=>[1,3,2,4]
[(1,4),(2,3)]=>[4,3,2,1]=>[1,4,2,3]=>[1,4,2,3]
[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]
[(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]
[(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]
[(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[1,6,2,4,3,5]=>[1,6,2,4,3,5]
[(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[1,5,2,4,3,6]=>[1,5,2,4,3,6]
[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[1,4,2,5,3,6]=>[1,4,2,5,3,6]
[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]
[(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]
[(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[1,4,2,6,3,5]=>[1,4,2,6,3,5]
[(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[1,5,2,6,3,4]=>[1,5,2,6,3,4]
[(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[1,6,2,5,3,4]=>[1,6,2,5,3,4]
[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[1,4,2,5,3,6,7,8]=>[1,4,2,5,3,6,7,8]
[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]
[(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[1,5,2,8,3,4,6,7]=>[1,5,2,8,3,4,6,7]
[(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[1,7,2,8,3,4,5,6]=>[1,7,2,8,3,4,5,6]
[(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[1,8,2,7,3,4,5,6]=>[1,8,2,7,3,4,5,6]
[(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[1,6,2,8,3,5,4,7]=>[1,6,2,8,3,5,4,7]
[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[1,5,2,6,3,7,4,8]=>[1,5,2,6,3,7,4,8]
[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[1,4,2,6,3,7,5,8]=>[1,4,2,6,3,7,5,8]
[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,4,7,5,8]
[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,4,7,5,8]
[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[1,4,2,5,3,7,6,8]=>[1,4,2,5,3,7,6,8]
[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[1,4,2,5,3,8,6,7]=>[1,4,2,5,3,8,6,7]
[(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]
[(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[1,6,2,7,3,8,4,5]=>[1,6,2,7,3,8,4,5]
          

Map

to permutation

Description

Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.

Map

cycle-as-one-line notation

Description

Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.

Map

runsort

Description

The permutation obtained by sorting the increasing runs lexicographically.