Identifier
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-3
[.,.]=>[.,.]=>[1]=>[.,.]=>[1] [.,[.,.]]=>[[.,.],.]=>[1,2]=>[.,[.,.]]=>[2,1] [[.,.],.]=>[.,[.,.]]=>[2,1]=>[[.,.],.]=>[1,2] [.,[.,[.,.]]]=>[[[.,.],.],.]=>[1,2,3]=>[.,[.,[.,.]]]=>[3,2,1] [.,[[.,.],.]]=>[[.,[.,.]],.]=>[2,1,3]=>[[.,.],[.,.]]=>[1,3,2] [[.,.],[.,.]]=>[[.,.],[.,.]]=>[3,1,2]=>[[.,.],[.,.]]=>[1,3,2] [[.,[.,.]],.]=>[.,[[.,.],.]]=>[2,3,1]=>[[.,[.,.]],.]=>[2,1,3] [[[.,.],.],.]=>[.,[.,[.,.]]]=>[3,2,1]=>[[[.,.],.],.]=>[1,2,3] [.,[.,[.,[.,.]]]]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1] [.,[.,[[.,.],.]]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2] [.,[[.,.],[.,.]]]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2] [.,[[.,[.,.]],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]=>[2,1,4,3] [.,[[[.,.],.],.]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[1,2,4,3] [[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[1,4,3,2] [[.,.],[[.,.],.]]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>[1,2,4,3] [[.,[.,.]],[.,.]]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[2,1,4,3] [[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>[1,2,4,3] [[.,[.,[.,.]]],.]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]=>[3,2,1,4] [[.,[[.,.],.]],.]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[[[.,.],[.,.]],.]=>[1,3,2,4] [[[.,.],[.,.]],.]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[[[.,.],[.,.]],.]=>[1,3,2,4] [[[.,[.,.]],.],.]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[[[.,[.,.]],.],.]=>[2,1,3,4] [[[[.,.],.],.],.]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,2,3,4] [.,[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1] [.,[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [.,[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [.,[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [.,[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [.,[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [.,[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [.,[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [.,[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [.,[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4] [.,[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [.,[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [.,[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4] [.,[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2] [[.,.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[.,.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[.,.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3] [[.,[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4] [[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3] [[[.,.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[.,[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4] [[.,[[.,.],.]],[.,.]]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4] [[[.,[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4] [[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4] [[.,[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5] [[.,[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5] [[.,[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5] [[.,[[.,[.,.]],.]],.]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5] [[.,[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5] [[[.,.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5] [[[.,.],[[.,.],.]],.]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5] [[[.,[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5] [[[[.,.],.],[.,.]],.]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5] [[[.,[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5] [[[.,[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5] [[[[.,.],[.,.]],.],.]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5] [[[[.,[.,.]],.],.],.]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5] [[[[[.,.],.],.],.],.]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5] [.,[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1] [.,[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [.,[.,[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [.,[.,[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [.,[.,[.,[[[.,.],.],.]]]]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [.,[.,[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2] [.,[.,[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [.,[.,[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3] [.,[.,[[[.,.],.],[.,.]]]]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3] [.,[.,[[.,[.,[.,.]]],.]]]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4] [.,[.,[[.,[[.,.],.]],.]]]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4] 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[.,[.,[[[[.,.],[.,.]],.],.]]]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [.,[.,[[[[.,[.,.]],.],.],.]]]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [.,[.,[[[[[.,.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2] [.,[[.,.],[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [.,[[.,.],[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [.,[[.,.],[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] 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[.,[[.,.],[[[.,.],[.,.]],.]]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [.,[[.,.],[[[[.,.],.],.],.]]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [.,[[.,[.,.]],[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [.,[[.,[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [.,[[.,[.,.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] 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[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5] [.,[[.,[[.,.],.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [.,[[.,[[.,.],.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [.,[[[.,.],[.,.]],[.,[.,.]]]]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [.,[[[.,.],[.,.]],[[.,.],.]]]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [.,[[[.,[.,.]],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [.,[[[.,[.,.]],.],[[.,.],.]]]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] 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[[.,.],[[[.,.],[.,[.,.]]],.]]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6] [[.,.],[[[.,.],[[.,.],.]],.]]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[.,.],[[[[.,.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6] [[.,.],[[[.,[[.,.],.]],.],.]]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6] [[.,.],[[[[.,.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6] [[.,.],[[[[.,[.,.]],.],.],.]]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6] [[.,.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6] [[.,[.,.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5] [[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6] [[[.,.],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[[.,.],.],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[[.,.],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6] [[[.,.],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[.,[[.,.],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6] [[[.,.],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6] [[[.,[.,.]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4] [[[[.,.],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[[[.,.],.],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[[[.,.],.],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6] [[[[.,.],.],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6] 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[[[[.,.],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7] [[[[.,.],[[.,[.,.]],.]],.],.]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7] [[[[.,.],[[[.,.],.],.]],.],.]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7] [[[[.,[.,.]],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7] [[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7] [[[[[.,.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7] [[[[.,[[.,.],.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7] [[[[[.,.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7] [[[[[.,[.,.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7] [[[[[[.,.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7] [[[[.,[.,[[.,.],.]]],.],.],.]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7] [[[[.,[[.,.],[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7] [[[[.,[[.,[.,.]],.]],.],.],.]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7] [[[[.,[[[.,.],.],.]],.],.],.]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7] [[[[[.,.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7] [[[[[.,.],[[.,.],.]],.],.],.]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7] [[[[[.,[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7] [[[[[[.,.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7] [[[[[.,[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7] [[[[[.,[[.,.],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7] [[[[[[.,.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7] [[[[[[.,[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7] [[[[[[[.,.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1] [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3] [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5] [[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6] [[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7] [[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6] [[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7] [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5] [[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6] [[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7] [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7] [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7] [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7] [[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7] [[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7] [[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8] [[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8] [[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8] [[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.
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
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.