Identifier
Mp00058: Perfect matchings to permutationPermutations
Mp00069: Permutations complementPermutations
Mp00065: Permutations permutation poset Posets
Images
=>
Cc0012;cc-rep-0Cc0014;cc-rep-3
[(1,2)]=>[2,1]=>[1,2]=>([(0,1)],2) [(1,2),(3,4)]=>[2,1,4,3]=>[3,4,1,2]=>([(0,3),(1,2)],4) [(1,3),(2,4)]=>[3,4,1,2]=>[2,1,4,3]=>([(0,2),(0,3),(1,2),(1,3)],4) [(1,4),(2,3)]=>[4,3,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4) [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>([(0,5),(1,4),(2,3)],6) [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3)],6) [(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>([(0,5),(1,3),(4,2),(5,4)],6) [(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) [(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) [(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) [(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5)],6) [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3)],6) [(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>([(0,5),(1,3),(4,2),(5,4)],6) [(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) [(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) [(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6) [(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>([(0,7),(1,6),(2,5),(3,4)],8) [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) [(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>([(0,5),(1,4),(2,7),(6,3),(7,6)],8) [(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>[4,6,7,3,8,5,1,2]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8) [(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[3,6,7,4,5,8,1,2]=>([(0,4),(1,5),(1,6),(2,7),(3,7),(5,3),(6,2)],8) [(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>[2,6,7,4,5,1,8,3]=>([(0,6),(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2)],8) [(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>([(0,4),(0,5),(0,6),(1,7),(2,7),(3,7),(4,3),(5,2),(6,1)],8) [(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>[1,5,4,7,6,2,3,8]=>([(0,2),(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7)],8) [(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>[2,5,4,7,6,1,8,3]=>([(0,6),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7)],8) [(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>[3,5,4,7,6,8,1,2]=>([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7)],8) [(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>[4,5,3,7,8,6,1,2]=>([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8) [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4)],8) [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]=>([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4)],8) [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) [(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>([(0,5),(1,4),(2,7),(6,3),(7,6)],8) [(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>[6,3,8,4,5,7,1,2]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8) [(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>[5,3,4,8,6,7,1,2]=>([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8) [(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>[4,3,5,6,8,7,1,2]=>([(0,7),(1,7),(2,5),(6,3),(6,4),(7,6)],8) [(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8) [(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>[2,4,5,6,7,1,8,3]=>([(0,6),(0,7),(1,5),(1,7),(2,6),(3,4),(4,2),(5,3)],8) [(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[1,4,5,6,7,2,3,8]=>([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8) [(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>[1,3,5,6,2,7,4,8]=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6),(5,7),(6,7)],8) [(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>[2,3,5,6,1,7,8,4]=>([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8) [(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>[3,2,5,6,1,8,7,4]=>([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,3)],8) [(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>[4,2,5,6,8,1,7,3]=>([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7),(6,3)],8) [(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>[5,2,4,8,6,1,7,3]=>([(0,3),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(7,4)],8) [(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>([(0,6),(0,7),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8) [(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>[7,8,2,4,5,1,6,3]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8) [(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[7,8,1,4,5,2,3,6]=>([(0,4),(1,5),(1,6),(2,7),(3,7),(5,3),(6,2)],8) [(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>[6,1,8,4,5,2,3,7]=>([(0,6),(0,7),(1,4),(1,5),(1,6),(2,7),(3,7),(4,3),(5,2)],8) [(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>[5,1,4,8,6,2,3,7]=>([(0,6),(0,7),(1,3),(1,4),(2,5),(3,6),(3,7),(4,2),(7,5)],8) [(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[4,1,5,6,8,2,3,7]=>([(0,7),(1,4),(1,7),(3,6),(4,3),(5,2),(5,6),(7,5)],8) [(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>[3,1,5,6,2,8,4,7]=>([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8) [(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(6,3),(7,2)],8) [(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>([(0,6),(1,7),(2,7),(4,2),(5,1),(6,4),(6,5),(7,3)],8) [(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(5,7),(6,7),(7,1)],8) [(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) [(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[3,1,4,2,6,8,5,7]=>([(0,7),(1,3),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5),(7,6)],8) [(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>[4,1,3,2,8,6,5,7]=>([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8) [(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>[5,1,3,8,2,6,4,7]=>([(0,2),(0,3),(1,4),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8) [(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>[6,1,8,3,2,5,4,7]=>([(0,6),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,7),(5,7)],8) [(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>[7,8,1,3,2,5,4,6]=>([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,7),(6,7)],8) [(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>[7,8,2,3,1,5,6,4]=>([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8) [(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>[6,2,8,3,1,5,7,4]=>([(0,3),(0,5),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(7,4)],8) [(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>([(0,6),(0,7),(1,5),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8) [(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8) [(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8) [(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8) [(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8) [(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(5,4),(6,4),(7,4)],8) [(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>([(0,2),(0,3),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(6,4),(7,4)],8) [(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8) [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7)],8) [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4)],8) [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]=>([(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4)],8) [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7)],8) [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7)],8) [(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>[4,5,2,7,8,1,6,3]=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(4,6),(4,7),(6,3)],8) [(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>[3,5,2,7,1,8,6,4]=>([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4)],8) [(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>[2,5,3,7,1,6,8,4]=>([(0,2),(0,3),(1,4),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(6,5),(7,5)],8) [(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4,8]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8) [(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>[1,6,7,3,2,5,4,8]=>([(0,2),(0,3),(0,4),(1,7),(2,5),(2,6),(3,5),(3,6),(4,1),(5,7),(6,7)],8) [(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>[2,6,7,3,1,5,8,4]=>([(0,6),(0,7),(1,3),(1,4),(2,5),(3,6),(3,7),(4,2),(7,5)],8) [(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>[3,6,7,2,1,8,5,4]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8) [(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>[4,6,7,2,8,1,5,3]=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(4,6)],8) [(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>[5,6,7,8,2,1,4,3]=>([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4)],8) [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7)],8) [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]=>([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4)],8) [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>([(0,5),(1,4),(2,7),(6,3),(7,6)],8) [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>[6,5,8,7,1,2,3,4]=>([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(5,4)],8) [(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) [(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>([(0,5),(0,7),(1,4),(1,6),(2,7),(3,6),(4,2),(5,3)],8) [(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>[3,6,7,1,2,8,4,5]=>([(0,4),(1,5),(1,7),(3,6),(4,6),(4,7),(5,3),(7,2)],8) [(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>[2,6,7,1,3,4,8,5]=>([(0,7),(1,4),(1,7),(3,6),(4,3),(5,2),(5,6),(7,5)],8) [(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[1,6,7,2,3,4,5,8]=>([(0,5),(0,6),(1,7),(2,7),(3,4),(4,2),(5,3),(6,1)],8) [(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>[1,5,2,7,3,4,6,8]=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6),(5,7),(6,7)],8) [(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>[2,5,1,7,3,4,8,6]=>([(0,3),(0,6),(1,6),(1,7),(2,4),(2,5),(3,4),(3,7),(6,2),(7,5)],8) [(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>([(0,3),(0,7),(1,2),(1,6),(2,4),(2,7),(3,5),(3,6),(6,4),(7,5)],8) [(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>[4,5,1,7,8,2,3,6]=>([(0,4),(1,5),(1,7),(3,6),(4,6),(4,7),(5,3),(7,2)],8) [(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[5,4,1,8,7,2,3,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,4),(4,7)],8) [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>[6,4,8,1,7,2,3,5]=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(4,6)],8) [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>[7,8,4,1,6,2,3,5]=>([(0,6),(0,7),(1,3),(2,4),(2,6),(4,5),(5,7)],8) [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>[7,8,3,1,2,6,4,5]=>([(0,6),(0,7),(1,3),(2,5),(5,6),(5,7),(7,4)],8) [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>[6,3,8,1,2,7,4,5]=>([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(4,6),(4,7),(6,3)],8) [(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[5,3,1,8,2,7,4,6]=>([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(3,5),(3,7),(5,4)],8) [(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>[4,3,1,2,8,7,5,6]=>([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8) [(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>([(0,5),(1,4),(4,6),(4,7),(5,6),(5,7),(6,3),(7,2)],8) [(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>[2,4,1,3,7,5,8,6]=>([(0,7),(1,3),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5),(7,6)],8) [(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>[1,4,2,3,7,5,6,8]=>([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8) [(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>([(0,3),(0,4),(1,6),(2,6),(3,7),(4,7),(5,1),(5,2),(7,5)],8) [(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8) [(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>([(0,7),(1,7),(2,7),(6,3),(6,4),(6,5),(7,6)],8) [(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>[4,2,1,3,8,5,7,6]=>([(0,6),(0,7),(1,5),(2,5),(5,6),(5,7),(7,3),(7,4)],8) [(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>[5,2,1,8,3,4,7,6]=>([(0,4),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,3)],8) [(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>[6,2,8,1,3,4,7,5]=>([(0,6),(1,5),(1,6),(2,5),(2,7),(3,4),(3,7),(6,3)],8) [(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>[7,8,2,1,3,4,6,5]=>([(0,7),(1,7),(2,5),(6,3),(6,4),(7,6)],8) [(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>([(0,7),(1,3),(4,6),(5,4),(6,2),(7,5)],8) [(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>[6,1,8,2,3,4,5,7]=>([(0,6),(0,7),(1,5),(1,7),(2,6),(3,4),(4,2),(5,3)],8) [(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>[5,1,2,8,3,4,6,7]=>([(0,6),(0,7),(1,5),(3,7),(4,3),(5,4),(5,6),(7,2)],8) [(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>[4,1,2,3,8,5,6,7]=>([(0,6),(0,7),(1,4),(3,6),(3,7),(4,3),(5,2),(7,5)],8) [(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>[3,1,2,4,5,8,6,7]=>([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8) [(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>([(0,7),(1,7),(4,6),(5,4),(6,2),(6,3),(7,5)],8) [(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$