Identifier
Mp00058: to permutationPermutations
Mp00061: Permutations to increasing treeBinary trees
Mp00016: left-right symmetry
Images
=>
Cc0012;cc-rep-0Cc0010;cc-rep-2Cc0010;cc-rep-3
[(1,2)]=>[2,1]=>[[.,.],.]=>[.,[.,.]] [(1,2),(3,4)]=>[2,1,4,3]=>[[.,.],[[.,.],.]]=>[[.,[.,.]],[.,.]] [(1,3),(2,4)]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[[.,.],[[.,.],.]] [(1,4),(2,3)]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[.,[.,[.,[.,.]]]] [(1,2),(3,4),(5,6)]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,.]] [(1,3),(2,4),(5,6)]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],.]] [(1,4),(2,3),(5,6)]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,.]]]] [(1,5),(2,3),(4,6)]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]] [(1,6),(2,3),(4,5)]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,.]]]] [(1,6),(2,4),(3,5)]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,.]]]] [(1,5),(2,4),(3,6)]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]] [(1,4),(2,5),(3,6)]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]] [(1,3),(2,5),(4,6)]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],.]] [(1,2),(3,5),(4,6)]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,.]] [(1,2),(3,6),(4,5)]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,.]] [(1,3),(2,6),(4,5)]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],.]] [(1,4),(2,6),(3,5)]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],.]] [(1,5),(2,6),(3,4)]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],.]]]] [(1,6),(2,5),(3,4)]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,.]]]]]] [(1,2),(3,4),(5,6),(7,8)]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [(1,3),(2,4),(5,6),(7,8)]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]] [(1,4),(2,3),(5,6),(7,8)]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [(1,5),(2,3),(4,6),(7,8)]=>[5,3,2,6,1,4,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]] [(1,6),(2,3),(4,5),(7,8)]=>[6,3,2,5,4,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [(1,7),(2,3),(4,5),(6,8)]=>[7,3,2,5,4,8,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]] [(1,8),(2,3),(4,5),(6,7)]=>[8,3,2,5,4,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] [(1,8),(2,4),(3,5),(6,7)]=>[8,4,5,2,3,7,6,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]] [(1,7),(2,4),(3,5),(6,8)]=>[7,4,5,2,3,8,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [(1,6),(2,4),(3,5),(7,8)]=>[6,4,5,2,3,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [(1,5),(2,4),(3,6),(7,8)]=>[5,4,6,2,1,3,8,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]] [(1,4),(2,5),(3,6),(7,8)]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]] [(1,3),(2,5),(4,6),(7,8)]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]] [(1,2),(3,5),(4,6),(7,8)]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]] [(1,2),(3,6),(4,5),(7,8)]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [(1,3),(2,6),(4,5),(7,8)]=>[3,6,1,5,4,2,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] [(1,4),(2,6),(3,5),(7,8)]=>[4,6,5,1,3,2,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]] [(1,5),(2,6),(3,4),(7,8)]=>[5,6,4,3,1,2,8,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] [(1,6),(2,5),(3,4),(7,8)]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [(1,7),(2,5),(3,4),(6,8)]=>[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [(1,8),(2,5),(3,4),(6,7)]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] [(1,8),(2,6),(3,4),(5,7)]=>[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] [(1,7),(2,6),(3,4),(5,8)]=>[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [(1,6),(2,7),(3,4),(5,8)]=>[6,7,4,3,8,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]] [(1,5),(2,7),(3,4),(6,8)]=>[5,7,4,3,1,8,2,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]] [(1,4),(2,7),(3,5),(6,8)]=>[4,7,5,1,3,8,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]] [(1,3),(2,7),(4,5),(6,8)]=>[3,7,1,5,4,8,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]] [(1,2),(3,7),(4,5),(6,8)]=>[2,1,7,5,4,8,3,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]] [(1,2),(3,8),(4,5),(6,7)]=>[2,1,8,5,4,7,6,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] [(1,3),(2,8),(4,5),(6,7)]=>[3,8,1,5,4,7,6,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]] [(1,4),(2,8),(3,5),(6,7)]=>[4,8,5,1,3,7,6,2]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]] [(1,5),(2,8),(3,4),(6,7)]=>[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] [(1,6),(2,8),(3,4),(5,7)]=>[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]] [(1,7),(2,8),(3,4),(5,6)]=>[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]] [(1,8),(2,7),(3,4),(5,6)]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] [(1,8),(2,7),(3,5),(4,6)]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [(1,7),(2,8),(3,5),(4,6)]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [(1,6),(2,8),(3,5),(4,7)]=>[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]] [(1,5),(2,8),(3,6),(4,7)]=>[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]] [(1,4),(2,8),(3,6),(5,7)]=>[4,8,6,1,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]] [(1,3),(2,8),(4,6),(5,7)]=>[3,8,1,6,7,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]] [(1,2),(3,8),(4,6),(5,7)]=>[2,1,8,6,7,4,5,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]] [(1,2),(3,7),(4,6),(5,8)]=>[2,1,7,6,8,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]] [(1,3),(2,7),(4,6),(5,8)]=>[3,7,1,6,8,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]] [(1,4),(2,7),(3,6),(5,8)]=>[4,7,6,1,8,3,2,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]] [(1,5),(2,7),(3,6),(4,8)]=>[5,7,6,8,1,3,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]] [(1,6),(2,7),(3,5),(4,8)]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]] [(1,7),(2,6),(3,5),(4,8)]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [(1,8),(2,6),(3,5),(4,7)]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] [(1,8),(2,5),(3,6),(4,7)]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [(1,7),(2,5),(3,6),(4,8)]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]] [(1,6),(2,5),(3,7),(4,8)]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]] [(1,5),(2,6),(3,7),(4,8)]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]] [(1,4),(2,6),(3,7),(5,8)]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]] [(1,3),(2,6),(4,7),(5,8)]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]] [(1,2),(3,6),(4,7),(5,8)]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]] [(1,2),(3,5),(4,7),(6,8)]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]] [(1,3),(2,5),(4,7),(6,8)]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]] [(1,4),(2,5),(3,7),(6,8)]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]] [(1,5),(2,4),(3,7),(6,8)]=>[5,4,7,2,1,8,3,6]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]] [(1,6),(2,4),(3,7),(5,8)]=>[6,4,7,2,8,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [(1,7),(2,4),(3,6),(5,8)]=>[7,4,6,2,8,3,1,5]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [(1,8),(2,4),(3,6),(5,7)]=>[8,4,6,2,7,3,5,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]] [(1,8),(2,3),(4,6),(5,7)]=>[8,3,2,6,7,4,5,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]] [(1,7),(2,3),(4,6),(5,8)]=>[7,3,2,6,8,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]] [(1,6),(2,3),(4,7),(5,8)]=>[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]] [(1,5),(2,3),(4,7),(6,8)]=>[5,3,2,7,1,8,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]] [(1,4),(2,3),(5,7),(6,8)]=>[4,3,2,1,7,8,5,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]] [(1,3),(2,4),(5,7),(6,8)]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]] [(1,2),(3,4),(5,7),(6,8)]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]] [(1,2),(3,4),(5,8),(6,7)]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [(1,3),(2,4),(5,8),(6,7)]=>[3,4,1,2,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] [(1,4),(2,3),(5,8),(6,7)]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [(1,5),(2,3),(4,8),(6,7)]=>[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] [(1,6),(2,3),(4,8),(5,7)]=>[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] [(1,7),(2,3),(4,8),(5,6)]=>[7,3,2,8,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] [(1,8),(2,3),(4,7),(5,6)]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] [(1,8),(2,4),(3,7),(5,6)]=>[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] [(1,7),(2,4),(3,8),(5,6)]=>[7,4,8,2,6,5,1,3]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]] [(1,6),(2,4),(3,8),(5,7)]=>[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]] [(1,5),(2,4),(3,8),(6,7)]=>[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] [(1,4),(2,5),(3,8),(6,7)]=>[4,5,8,1,2,7,6,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]] [(1,3),(2,5),(4,8),(6,7)]=>[3,5,1,8,2,7,6,4]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]] [(1,2),(3,5),(4,8),(6,7)]=>[2,1,5,8,3,7,6,4]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]] [(1,2),(3,6),(4,8),(5,7)]=>[2,1,6,8,7,3,5,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]] [(1,3),(2,6),(4,8),(5,7)]=>[3,6,1,8,7,2,5,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] [(1,4),(2,6),(3,8),(5,7)]=>[4,6,8,1,7,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]] [(1,5),(2,6),(3,8),(4,7)]=>[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]] [(1,6),(2,5),(3,8),(4,7)]=>[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] [(1,7),(2,5),(3,8),(4,6)]=>[7,5,8,6,2,4,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]] [(1,8),(2,5),(3,7),(4,6)]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] [(1,8),(2,6),(3,7),(4,5)]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [(1,7),(2,6),(3,8),(4,5)]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [(1,6),(2,7),(3,8),(4,5)]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [(1,5),(2,7),(3,8),(4,6)]=>[5,7,8,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]] [(1,4),(2,7),(3,8),(5,6)]=>[4,7,8,1,6,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]] [(1,3),(2,7),(4,8),(5,6)]=>[3,7,1,8,6,5,2,4]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]] [(1,2),(3,7),(4,8),(5,6)]=>[2,1,7,8,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]] [(1,2),(3,8),(4,7),(5,6)]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [(1,3),(2,8),(4,7),(5,6)]=>[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] [(1,4),(2,8),(3,7),(5,6)]=>[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] [(1,5),(2,8),(3,7),(4,6)]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] [(1,6),(2,8),(3,7),(4,5)]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] [(1,7),(2,8),(3,6),(4,5)]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [(1,8),(2,7),(3,6),(4,5)]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.