Identifier
Mp00058:
Perfect matchings
—to permutation⟶
Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Images
=>
Cc0012;cc-rep-0
[(1,2)]=>[2,1]=>[2,1]
[(1,2),(3,4)]=>[2,1,4,3]=>[2,1,4,3]
[(1,3),(2,4)]=>[3,4,1,2]=>[3,4,1,2]
[(1,4),(2,3)]=>[4,3,2,1]=>[4,3,2,1]
[(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[3,4,1,2,6,5]
[(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]
[(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]
[(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]
[(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]
[(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]
[(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]
[(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[3,5,1,6,2,4]
[(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[2,1,5,6,3,4]
[(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]
[(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]
[(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]
[(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]
[(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]
[(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]
[(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]
[(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>[5,3,2,6,1,4,8,7]
[(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[6,3,2,5,4,1,8,7]
[(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>[7,3,2,5,4,8,1,6]
[(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[8,3,2,5,4,7,6,1]
[(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>[8,4,5,2,3,7,6,1]
[(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>[7,4,5,2,3,8,1,6]
[(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>[6,4,5,2,3,1,8,7]
[(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>[5,4,6,2,1,3,8,7]
[(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[4,5,6,1,2,3,8,7]
[(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[3,5,1,6,2,4,8,7]
[(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[2,1,5,6,3,4,8,7]
[(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]
[(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>[3,6,1,5,4,2,8,7]
[(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>[4,6,5,1,3,2,8,7]
[(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>[5,6,4,3,1,2,8,7]
[(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]
[(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]
[(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]
[(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>[8,6,4,3,7,2,5,1]
[(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>[7,6,4,3,8,2,1,5]
[(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>[6,7,4,3,8,1,2,5]
[(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>[5,7,4,3,1,8,2,6]
[(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>[4,7,5,1,3,8,2,6]
[(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>[3,7,1,5,4,8,2,6]
[(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>[2,1,7,5,4,8,3,6]
[(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[2,1,8,5,4,7,6,3]
[(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>[3,8,1,5,4,7,6,2]
[(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>[4,8,5,1,3,7,6,2]
[(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[5,8,4,3,1,7,6,2]
[(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>[6,8,4,3,7,1,5,2]
[(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]
[(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]
[(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>[8,7,5,6,3,4,2,1]
[(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]
[(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[6,8,5,7,3,1,4,2]
[(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>[5,8,6,7,1,3,4,2]
[(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>[4,8,6,1,7,3,5,2]
[(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>[3,8,1,6,7,4,5,2]
[(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>[2,1,8,6,7,4,5,3]
[(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>[2,1,7,6,8,4,3,5]
[(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>[3,7,1,6,8,4,2,5]
[(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>[4,7,6,1,8,3,2,5]
[(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>[5,7,6,8,1,3,2,4]
[(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>[6,7,5,8,3,1,2,4]
[(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>[7,6,5,8,3,2,1,4]
[(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]
[(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]
[(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>[7,5,6,8,2,3,1,4]
[(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]
[(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]
[(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[4,6,7,1,8,2,3,5]
[(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[3,6,1,7,8,2,4,5]
[(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[2,1,6,7,8,3,4,5]
[(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[2,1,5,7,3,8,4,6]
[(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[3,5,1,7,2,8,4,6]
[(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[4,5,7,1,2,8,3,6]
[(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>[5,4,7,2,1,8,3,6]
[(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>[6,4,7,2,8,1,3,5]
[(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>[7,4,6,2,8,3,1,5]
[(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>[8,4,6,2,7,3,5,1]
[(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>[8,3,2,6,7,4,5,1]
[(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>[7,3,2,6,8,4,1,5]
[(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>[6,3,2,7,8,1,4,5]
[(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>[5,3,2,7,1,8,4,6]
[(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,7,8,5,6]
[(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[3,4,1,2,7,8,5,6]
[(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,7,8,5,6]
[(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]
[(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>[3,4,1,2,8,7,6,5]
[(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]
[(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]
[(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]
[(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>[7,3,2,8,6,5,1,4]
[(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]
[(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>[8,4,7,2,6,5,3,1]
[(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>[7,4,8,2,6,5,1,3]
[(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]
[(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]
[(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[4,5,8,1,2,7,6,3]
[(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>[3,5,1,8,2,7,6,4]
[(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>[2,1,5,8,3,7,6,4]
[(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>[2,1,6,8,7,3,5,4]
[(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>[3,6,1,8,7,2,5,4]
[(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[4,6,8,1,7,2,5,3]
[(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>[5,6,8,7,1,2,4,3]
[(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]
[(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>[7,5,8,6,2,4,1,3]
[(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>[8,5,7,6,2,4,3,1]
[(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>[8,6,7,5,4,2,3,1]
[(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]
[(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[6,7,8,5,4,1,2,3]
[(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>[5,7,8,6,1,4,2,3]
[(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>[4,7,8,1,6,5,2,3]
[(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>[3,7,1,8,6,5,2,4]
[(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>[2,1,7,8,6,5,3,4]
[(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]
[(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]
[(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]
[(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]
[(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>[6,8,7,5,4,1,3,2]
[(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>[7,8,6,5,4,3,1,2]
[(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[(1,6),(2,4),(3,5),(7,8),(9,10)]=>[6,4,5,2,3,1,8,7,10,9]=>[6,4,5,2,3,1,8,7,10,9]
[(1,8),(2,9),(3,5),(4,6),(7,10)]=>[8,9,5,6,3,4,10,1,2,7]=>[8,9,5,6,3,4,10,1,2,7]
[(1,2),(3,8),(4,6),(5,7),(9,10)]=>[2,1,8,6,7,4,5,3,10,9]=>[2,1,8,6,7,4,5,3,10,9]
[(1,9),(2,7),(3,6),(4,5),(8,10)]=>[9,7,6,5,4,3,2,10,1,8]=>[9,7,6,5,4,3,2,10,1,8]
[(1,10),(2,9),(3,8),(4,6),(5,7)]=>[10,9,8,6,7,4,5,3,2,1]=>[10,9,8,6,7,4,5,3,2,1]
[(1,10),(2,8),(3,9),(4,6),(5,7)]=>[10,8,9,6,7,4,5,2,3,1]=>[10,8,9,6,7,4,5,2,3,1]
[(1,2),(3,4),(5,10),(6,8),(7,9)]=>[2,1,4,3,10,8,9,6,7,5]=>[2,1,4,3,10,8,9,6,7,5]
[(1,6),(2,7),(3,8),(4,9),(5,10)]=>[6,7,8,9,10,1,2,3,4,5]=>[6,7,8,9,10,1,2,3,4,5]
[(1,7),(2,3),(4,8),(5,9),(6,10)]=>[7,3,2,8,9,10,1,4,5,6]=>[7,3,2,8,9,10,1,4,5,6]
[(1,8),(2,5),(3,4),(6,9),(7,10)]=>[8,5,4,3,2,9,10,1,6,7]=>[8,5,4,3,2,9,10,1,6,7]
[(1,6),(2,5),(3,4),(7,10),(8,9)]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]
[(1,9),(2,7),(3,5),(4,10),(6,8)]=>[9,7,5,10,3,8,2,6,1,4]=>[9,7,5,10,3,8,2,6,1,4]
[(1,10),(2,8),(3,9),(4,7),(5,6)]=>[10,8,9,7,6,5,4,2,3,1]=>[10,8,9,7,6,5,4,2,3,1]
[(1,10),(2,9),(3,8),(4,7),(5,6)]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[7,8,9,10,11,12,1,2,3,4,5,6]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
inverse
Description
Sends a permutation to its inverse.
searching the database
Sorry, this map was not found in the database.