Identifier
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00108: Permutations —cycle type⟶ Integer partitions
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0002;cc-rep-3
[.,.]=>[.,.]=>[1]=>[1] [.,[.,.]]=>[.,[.,.]]=>[2,1]=>[2] [[.,.],.]=>[[.,.],.]=>[1,2]=>[1,1] [.,[.,[.,.]]]=>[.,[.,[.,.]]]=>[3,2,1]=>[2,1] [.,[[.,.],.]]=>[.,[[.,.],.]]=>[2,3,1]=>[3] [[.,.],[.,.]]=>[[.,[.,.]],.]=>[2,1,3]=>[2,1] [[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,3,2]=>[2,1] [[[.,.],.],.]=>[[[.,.],.],.]=>[1,2,3]=>[1,1,1] [.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,2] [.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4] [.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,1] [.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[3,1] [.,[[[.,.],.],.]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4] [[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,1,1] [[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1] [[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,2] [[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,1] [[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[2,1,1] [[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1] [[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>[2,1,1] [[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>[2,1,1] [[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,1,1,1] [.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,2,1] [.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,1] [.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5] [.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5] [.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,2] [.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[3,2] [.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5] [.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[3,1,1] [.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[4,1] [.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[3,2] [.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5] [.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,1] [.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[4,1] [.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5] [[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,2,1] [[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1] [[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,1,1] [[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[3,1,1] [[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1] [[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[2,2,1] [[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2] [[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,1,1,1] [[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,1] [[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,2,1] [[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[3,2] [[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,2,1] [[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,2,1] [[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,1,1] [[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[2,2,1] [[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,1] [[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[3,1,1] [[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[3,1,1] [[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[4,1] [[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[2,1,1,1] [[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,1] [[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[2,2,1] [[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[2,1,1,1] [[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[2,1,1,1] [[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[3,1,1] [[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[2,1,1,1] [[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[2,1,1,1] [[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,1,1,1,1] [.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[2,2,2] [.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[4,2] [.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6] [.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6] [.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,2] [.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,1] [.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[3,2,1] [.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6] [.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[3,3] [.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[5,1] [.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[3,2,1] [.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[4,2] [.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[3,3] [.,[.,[[[[.,.],.],.],.]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6] [.,[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[3,2,1] [.,[[.,.],[.,[[.,.],.]]]]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[5,1] [.,[[.,.],[[.,.],[.,.]]]]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6] [.,[[.,.],[[.,[.,.]],.]]]=>[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6] [.,[[.,.],[[[.,.],.],.]]]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[4,2] [.,[[.,[.,.]],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[3,2,1] [.,[[.,[.,.]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[5,1] [.,[[[.,.],.],[.,[.,.]]]]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,2] [.,[[[.,.],.],[[.,.],.]]]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6] [.,[[.,[.,[.,.]]],[.,.]]]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[3,2,1] [.,[[.,[[.,.],.]],[.,.]]]=>[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,1] [.,[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[4,1,1] [.,[[[.,[.,.]],.],[.,.]]]=>[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[4,1,1] [.,[[[[.,.],.],.],[.,.]]]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[5,1] [.,[[.,[.,[.,[.,.]]]],.]]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[3,2,1] [.,[[.,[.,[[.,.],.]]],.]]=>[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,1] [.,[[.,[[.,.],[.,.]]],.]]=>[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6] [.,[[.,[[.,[.,.]],.]],.]]=>[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6] [.,[[.,[[[.,.],.],.]],.]]=>[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2] [.,[[[.,.],[.,[.,.]]],.]]=>[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[4,2] [.,[[[.,.],[[.,.],.]],.]]=>[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6] [.,[[[.,[.,.]],[.,.]],.]]=>[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[4,1,1] [.,[[[[.,.],.],[.,.]],.]]=>[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[5,1] [.,[[[.,[.,[.,.]]],.],.]]=>[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[4,2] [.,[[[.,[[.,.],.]],.],.]]=>[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6] 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[[.,.],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,1] [[.,.],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,1,1] [[.,.],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[4,1,1] [[.,.],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1] [[.,[.,.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[2,2,2] [[.,[.,.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,2] [[.,[.,.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[3,2,1] [[.,[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[3,2,1] [[.,[.,.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2] [[[.,.],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[2,2,1,1] [[[.,.],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,1,1] [[[.,.],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,1,1,1] [[[.,.],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[3,1,1,1] [[[.,.],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,1] [[.,[.,[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[2,2,1,1] [[.,[.,[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1] [[.,[[.,.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1] [[.,[[.,.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,3] [[[.,.],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[2,2,1,1] [[[.,.],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,2,1] [[[.,[.,.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[2,2,1,1] [[[.,[.,.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,2,1] [[[[.,.],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[2,1,1,1,1] [[[[.,.],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,1,1] [[.,[.,[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,2,2] [[.,[.,[[.,.],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[4,2] [[.,[[.,.],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[3,2,1] [[.,[[.,[.,.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[3,2,1] [[.,[[[.,.],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2] [[[.,.],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,2,1,1] [[[.,.],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[3,2,1] [[[.,[.,.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,2,2] [[[[.,.],.],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,2,1,1] [[[.,[.,[.,.]]],.],[.,.]]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,2,1,1] [[[.,[[.,.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[3,2,1] [[[[.,.],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,2,1,1] [[[[.,[.,.]],.],.],[.,.]]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,2,1,1] [[[[[.,.],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,1,1,1] [[.,[.,[.,[.,[.,.]]]]],.]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[2,2,1,1] [[.,[.,[.,[[.,.],.]]]],.]=>[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[4,1,1] [[.,[.,[[.,.],[.,.]]]],.]=>[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,1] [[.,[.,[[.,[.,.]],.]]],.]=>[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[5,1] [[.,[.,[[[.,.],.],.]]],.]=>[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[3,2,1] [[.,[[.,.],[.,[.,.]]]],.]=>[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[3,2,1] [[.,[[.,.],[[.,.],.]]],.]=>[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[5,1] [[.,[[.,[.,.]],[.,.]]],.]=>[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[3,1,1,1] [[.,[[[.,.],.],[.,.]]],.]=>[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,1,1] [[.,[[.,[.,[.,.]]],.]],.]=>[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[3,2,1] [[.,[[.,[[.,.],.]],.]],.]=>[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,1] [[.,[[[.,.],[.,.]],.]],.]=>[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[4,1,1] 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[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,1,1] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[3,2,1,1] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,1] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[3,3,1] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[5,1,1] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[3,2,1,1] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[4,2,1] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[3,3,1] [[.,.],[.,[[[[.,.],.],.],.]]]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,1] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[3,2,1,1] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[5,1,1] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,1] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,1] [[.,.],[[.,.],[[[.,.],.],.]]]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[4,2,1] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[3,2,1,1] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[5,1,1] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,2,1] [[.,.],[[[.,.],.],[[.,.],.]]]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,1] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[3,2,1,1] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[5,1,1] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[4,1,1,1] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[4,1,1,1] [[.,.],[[[[.,.],.],.],[.,.]]]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[5,1,1] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[3,2,1,1] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[5,1,1] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,1] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,1] [[.,.],[[.,[[[.,.],.],.]],.]]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,2,1] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[4,2,1] [[.,.],[[[.,.],[[.,.],.]],.]]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,1] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[4,1,1,1] [[.,.],[[[[.,.],.],[.,.]],.]]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[5,1,1] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[4,2,1] [[.,.],[[[.,[[.,.],.]],.],.]]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,1] [[.,.],[[[[.,.],[.,.]],.],.]]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[5,1,1] [[.,.],[[[[.,[.,.]],.],.],.]]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[5,1,1] [[.,.],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[2,2,2,1] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[4,2,1] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[5,2] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[5,2] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[3,2,2] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[3,2,2] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,2] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[3,2,1,1] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[4,2,1] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[3,2,2] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[5,2] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[4,2,1] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[4,2,1] [[.,[.,.]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,2] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[2,2,1,1,1] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,1,1,1] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,1,1] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,1,1] [[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,2,1,1] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[3,2,1,1] [[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,1,1] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[3,1,1,1,1] [[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[4,1,1,1] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[3,2,1,1] [[[.,.],.],[[.,[[.,.],.]],.]]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,1,1] [[[.,.],.],[[[.,.],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[4,1,1,1] [[[.,.],.],[[[.,[.,.]],.],.]]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[4,1,1,1] [[[.,.],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,1] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[2,2,2,1] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[4,2,1] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[3,2,1,1] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[3,2,1,1] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,2,1] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[3,2,2] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,3] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[3,3,1] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[3,3,1] [[.,[[.,.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,3] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[2,2,2,1] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,2,1] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[3,2,1,1] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[3,2,1,1] [[[.,.],[.,.]],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,2,1] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[2,2,2,1] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,2,1] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[3,2,1,1] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[3,2,1,1] [[[.,[.,.]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,2,1] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[2,2,1,1,1] [[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,1,1,1] [[[[.,.],.],.],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,1,1,1,1] [[[[.,.],.],.],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[3,1,1,1,1] [[[[.,.],.],.],[[[.,.],.],.]]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,1,1] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[2,2,2,1] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,2,2] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[4,2,1] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[4,3] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,1,1] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,3,1] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,1,1] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,3,1] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[4,2,1] [[.,[[[.,.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[4,3] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[2,2,1,1,1] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,2,1,1] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[3,2,1,1] [[[.,.],[[.,.],.]],[[.,.],.]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,3,1] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[2,2,2,1] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,2,2] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[2,2,1,1,1] [[[[.,.],.],[.,.]],[[.,.],.]]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,2,1,1] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[2,2,1,1,1] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,2,1,1] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,2,1,1] [[[.,[[.,.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,3,1] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[2,2,1,1,1] [[[[.,.],[.,.]],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,2,1,1] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[2,2,1,1,1] [[[[.,[.,.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,2,1,1] [[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[2,1,1,1,1,1] [[[[[.,.],.],.],.],[[.,.],.]]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,1,1,1] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,2,2,1] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[4,2,1] [[.,[.,[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[5,2] [[.,[.,[[.,[.,.]],.]]],[.,.]]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[5,2] [[.,[.,[[[.,.],.],.]]],[.,.]]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[3,2,2] [[.,[[.,.],[.,[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[3,2,2] [[.,[[.,.],[[.,.],.]]],[.,.]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[5,2] [[.,[[.,[.,.]],[.,.]]],[.,.]]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[3,2,1,1] [[.,[[[.,.],.],[.,.]]],[.,.]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[4,2,1] [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[3,2,2] [[.,[[.,[[.,.],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[5,2] [[.,[[[.,.],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[4,2,1] [[.,[[[.,[.,.]],.],.]],[.,.]]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[4,2,1] [[.,[[[[.,.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[5,2] [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,2,2,1] [[[.,.],[.,[[.,.],.]]],[.,.]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[4,2,1] [[[.,.],[[.,.],[.,.]]],[.,.]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[3,2,1,1] [[[.,.],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[3,2,1,1] [[[.,.],[[[.,.],.],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[4,2,1] [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,2,2,1] [[[.,[.,.]],[[.,.],.]],[.,.]]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[3,2,2] [[[[.,.],.],[.,[.,.]]],[.,.]]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,2,1,1,1] [[[[.,.],.],[[.,.],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[3,2,1,1] [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,2,2,1] [[[.,[[.,.],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[3,2,2] 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[[[.,[.,[[.,[.,.]],.]]],.],.]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[5,1,1] [[[.,[.,[[[.,.],.],.]]],.],.]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[3,2,1,1] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[3,2,1,1] [[[.,[[.,.],[[.,.],.]]],.],.]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,1,1] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[3,1,1,1,1] [[[.,[[[.,.],.],[.,.]]],.],.]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[4,1,1,1] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[3,2,1,1] [[[.,[[.,[[.,.],.]],.]],.],.]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[5,1,1] [[[.,[[[.,.],[.,.]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[4,1,1,1] [[[.,[[[.,[.,.]],.],.]],.],.]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[4,1,1,1] [[[.,[[[[.,.],.],.],.]],.],.]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[5,1,1] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[2,2,1,1,1] [[[[.,.],[.,[[.,.],.]]],.],.]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[4,1,1,1] [[[[.,.],[[.,.],[.,.]]],.],.]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[3,1,1,1,1] [[[[.,.],[[.,[.,.]],.]],.],.]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[3,1,1,1,1] [[[[.,.],[[[.,.],.],.]],.],.]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[4,1,1,1] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[2,2,1,1,1] [[[[.,[.,.]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[3,2,1,1] [[[[[.,.],.],[.,[.,.]]],.],.]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[2,1,1,1,1,1] [[[[[.,.],.],[[.,.],.]],.],.]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[3,1,1,1,1] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[2,2,1,1,1] [[[[.,[[.,.],.]],[.,.]],.],.]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[3,2,1,1] [[[[[.,.],[.,.]],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[2,2,1,1,1] [[[[[.,[.,.]],.],[.,.]],.],.]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[2,2,1,1,1] [[[[[[.,.],.],.],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[2,1,1,1,1,1] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[2,2,1,1,1] [[[[.,[.,[[.,.],.]]],.],.],.]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[4,1,1,1] [[[[.,[[.,.],[.,.]]],.],.],.]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[3,1,1,1,1] [[[[.,[[.,[.,.]],.]],.],.],.]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[3,1,1,1,1] [[[[.,[[[.,.],.],.]],.],.],.]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[4,1,1,1] [[[[[.,.],[.,[.,.]]],.],.],.]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[2,1,1,1,1,1] [[[[[.,.],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[3,1,1,1,1] [[[[[.,[.,.]],[.,.]],.],.],.]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[2,2,1,1,1] [[[[[[.,.],.],[.,.]],.],.],.]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[2,1,1,1,1,1] [[[[[.,[.,[.,.]]],.],.],.],.]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[2,1,1,1,1,1] [[[[[.,[[.,.],.]],.],.],.],.]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[3,1,1,1,1] [[[[[[.,.],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[2,1,1,1,1,1] [[[[[[.,[.,.]],.],.],.],.],.]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[2,1,1,1,1,1] [[[[[[[.,.],.],.],.],.],.],.]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,1,1,1,1,1,1] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[2,2,2,2] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[2,2,2,2] [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[2,2,2,2] [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,4] [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[3,3,1,1] [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[3,3,1,1] [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,4] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[2,2,2,2] [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[2,2,1,1,1,1] [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,3,1,1] [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,2,2,2] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,2,2,2] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,2,2,2] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,2,2,2] [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,2,1,1,1,1] [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[2,2,1,1,1,1] [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[3,3,1,1] [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[2,2,1,1,1,1] [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[2,2,1,1,1,1] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,1,1,1,1,1,1,1]
Map
left border symmetry
Description
Return the tree where a symmetry has been applied recursively on all left borders. If a tree is made of three trees $T_1, T_2, T_3$ on its left border, it becomes $T_3, T_2, T_1$ where same symmetry has been applied to $T_1, T_2, T_3$.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
cycle type
Description
The cycle type of a permutation as a partition.