Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0012;cc-rep-0Cc0010;cc-rep-3
[(1,2)]=>[2,1]=>[1,2]=>[.,[.,.]] [(1,2),(3,4)]=>[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [(1,3),(2,4)]=>[3,4,1,2]=>[2,1,4,3]=>[[.,.],[[.,.],.]] [(1,4),(2,3)]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[[[.,[.,.]],.],[[.,.],.]] [(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>[[.,.],[[.,.],[.,[.,.]]]] [(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]] [(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]] [(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,.]] [(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]] [(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]] [(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]] [(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>[4,6,7,3,8,5,1,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[3,6,7,4,5,8,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>[2,6,7,4,5,1,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] [(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>[1,5,4,7,6,2,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] [(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>[2,5,4,7,6,1,8,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>[3,5,4,7,6,8,1,2]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>[4,5,3,7,8,6,1,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]] [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]] [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]] [(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>[6,3,8,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] [(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>[5,3,4,8,6,7,1,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] [(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>[4,3,5,6,8,7,1,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] [(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>[2,4,5,6,7,1,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[1,4,5,6,7,2,3,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] [(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>[1,3,5,6,2,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] [(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>[2,3,5,6,1,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>[3,2,5,6,1,8,7,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]] [(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>[4,2,5,6,8,1,7,3]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] [(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>[5,2,4,8,6,1,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]] [(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]] [(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>[7,8,2,4,5,1,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] [(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[7,8,1,4,5,2,3,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] [(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>[6,1,8,4,5,2,3,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] [(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>[5,1,4,8,6,2,3,7]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] [(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[4,1,5,6,8,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>[3,1,5,6,2,8,4,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] [(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[3,1,4,2,6,8,5,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>[4,1,3,2,8,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]] [(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>[5,1,3,8,2,6,4,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] [(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>[6,1,8,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]] [(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>[7,8,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] [(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>[7,8,2,3,1,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] [(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>[6,2,8,3,1,5,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]] [(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] [(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]] [(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]] [(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] [(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]] [(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>[3,4,2,1,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]] [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]] [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]] [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]] [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]] [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]] [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]] [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]] [(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>[4,5,2,7,8,1,6,3]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] [(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>[3,5,2,7,1,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>[2,5,3,7,1,6,8,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] [(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>[1,6,7,3,2,5,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] [(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>[2,6,7,3,1,5,8,4]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] [(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>[3,6,7,2,1,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]] [(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>[4,6,7,2,8,1,5,3]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>[5,6,7,8,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]] [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]] [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>[6,5,8,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] [(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>[3,6,7,1,2,8,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>[2,6,7,1,3,4,8,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] [(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[1,6,7,2,3,4,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] [(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>[1,5,2,7,3,4,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] [(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>[2,5,1,7,3,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>[4,5,1,7,8,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[5,4,1,8,7,2,3,6]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]] [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>[6,4,8,1,7,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>[7,8,4,1,6,2,3,5]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>[7,8,3,1,2,6,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>[6,3,8,1,2,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] [(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[5,3,1,8,2,7,4,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]] [(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>[4,3,1,2,8,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]] [(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>[2,4,1,3,7,5,8,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>[4,2,1,3,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]] [(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>[5,2,1,8,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]] [(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>[6,2,8,1,3,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] [(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>[7,8,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] [(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>[6,1,8,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] [(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>[5,1,2,8,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] [(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [(1,2),(3,4),(5,6),(7,8),(9,10)]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
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
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.