Identifier
Mp00016: Binary trees left-right symmetryBinary trees
Mp00009: Binary trees left rotateBinary trees
Mp00017: Binary trees to 312-avoiding permutationPermutations
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
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[[.,[.,.]],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7] [[.,[.,.]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6] [[[.,.],.],[.,[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6] [[[.,.],.],[[.,.],[[.,.],.]]]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6] [[[.,.],.],[[[.,.],.],[.,.]]]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6] [[[.,.],.],[[.,[[.,.],.]],.]]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6] [[[.,.],.],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6] [[[.,.],.],[[[.,[.,.]],.],.]]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6] [[[.,.],.],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7] 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[[[.,.],[.,.]],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5] [[[.,[.,.]],.],[[[.,.],.],.]]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5] [[[[.,.],.],.],[.,[[.,.],.]]]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5] [[[[.,.],.],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5] 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[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],.]=>[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[2,4,6,5,8,7,3,10,9,1] [.,[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],.]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]=>[2,4,3,6,8,7,5,10,9,1] [.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],.]=>[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[2,4,6,8,7,5,3,10,9,1] [.,[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],.]=>[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[2,4,6,5,8,7,10,9,3,1] [.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]],.]=>[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[2,4,6,8,7,5,10,9,3,1] [.,[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>[2,4,3,6,8,7,10,9,5,1] [.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]=>[.,[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[2,4,6,8,7,10,9,5,3,1] [.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,5,8,10,9,7,1] [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[1,3,2,5,4,7,9,8,6,10] [[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],.]]]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[1,3,2,5,4,7,9,8,10,6] [[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]=>[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]]=>[1,3,2,5,4,7,9,10,8,6] [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,10,9,12,11,1] [.,[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]]=>[[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],.]=>[.,[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]]=>[2,4,6,5,3,8,7,10,9,12,11,1] [.,[[.,.],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]]]=>[[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],.]=>[.,[[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]]]=>[2,4,6,5,8,7,3,10,9,12,11,1] [.,[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],.]=>[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[2,4,3,6,8,7,5,10,9,12,11,1] [.,[[.,.],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]]]=>[[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],.]=>[.,[[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]]]=>[2,4,6,8,7,5,3,10,9,12,11,1] [.,[[.,.],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]]]=>[[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],.]=>[.,[[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]]=>[2,4,6,5,8,7,10,9,3,12,11,1] 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[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],.]=>[.,[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[2,4,3,6,8,10,9,12,11,7,5,1] [.,[[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]]=>[[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],.]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]]]=>[2,4,6,8,10,9,12,11,7,5,3,1] [.,[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,6,5,8,7,10,12,11,9,1] [.,[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]]]=>[[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[[.,.],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]]=>[2,4,6,5,3,8,7,10,12,11,9,1] [.,[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]]=>[[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]]=>[2,4,6,5,8,7,3,10,12,11,9,1] [.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[2,4,3,6,8,7,5,10,12,11,9,1] [.,[[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]]=>[[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],.]=>[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]]=>[2,4,6,5,8,7,10,12,11,9,3,1] [.,[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]]=>[2,4,3,6,5,8,10,12,11,9,7,1] [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,9,8,7,6,5,4,3,1] [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[2,1,8,9,7,6,5,4,3] [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[3,9,8,7,6,5,4,2,1] [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3] [.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]=>[7,6,5,4,3,8,2,9,1] [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1] [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9] [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2] [[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[1,8,7,6,5,4,3,9,2] [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[1,9,8,10,7,6,5,4,3,2] 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[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9] [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9] [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9] [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8] [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,1,4,6,8,10,9,7,5,3] [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11] 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[[[.,[[.,.],.]],[.,[[.,.],[[.,[[.,.],.]],.]]]],.]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[4,3,5,2,7,6,8,1,11,10,12,9] [[[.,[[.,.],.]],[.,[[.,[[.,.],.]],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],.]]]=>[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[3,2,6,5,7,4,8,1,11,10,12,9] [[[.,[[.,.],.]],[.,[[.,[[.,.],[[.,.],.]]],.]]],.]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]]=>[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[4,3,6,5,7,2,8,1,11,10,12,9] [[[.,[[.,.],[[.,.],.]]],[.,[[.,.],[[.,.],.]]]],.]=>[.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1,9,8,11,10,12,7] [[[.,[[.,.],[[.,.],.]]],[.,[[.,[[.,.],.]],.]]],.]=>[.,[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]]]=>[[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[4,3,5,2,6,1,9,8,11,10,12,7] [[[.,[[.,.],[[.,.],[[.,.],.]]]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]=>[[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,4,1,7,6,9,8,11,10,12,5] [[[.,[[.,.],[[.,[[.,.],.]],.]]],[.,[[.,.],.]]],.]=>[.,[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]=>[[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[3,2,4,1,8,7,9,6,11,10,12,5] [[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[.,.]],.]=>[.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]]=>[[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,9,8,11,10,12,3] [[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]]=>[[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[2,1,6,5,7,4,9,8,11,10,12,3] [[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]]=>[[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[2,1,5,4,8,7,9,6,11,10,12,3] [[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[.,.]],.]=>[.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]]=>[[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[2,1,6,5,8,7,9,4,11,10,12,3] [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4] [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[2,4,3,1,6,5,8,10,9,7] [[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]]=>[2,1,4,3,6,8,10,9,7,5] [[[.,.],[[[.,.],[.,.]],[.,.]]],[[.,.],.]]=>[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]]=>[2,1,4,6,8,7,5,3,10,9] [[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[2,1,4,6,8,10,12,11,9,7,5,3] [[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[2,4,3,1,6,8,7,10,12,11,9,5] [[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,1,4,3,6,8,10,12,11,9,7,5] [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5] [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6] [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7] [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5] [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6] [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7] [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8] [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3] [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9] [[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10] [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10] [[.,[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,[[.,.],.]],.]],.]],.]]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]=>[2,6,7,5,8,4,9,3,1,10] [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]],.]=>[.,[[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]]=>[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.]=>[2,7,8,6,9,5,10,4,11,3,1,12] [[[[[.,.],[.,.]],.],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]=>[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>[1,3,2,5,4,8,10,9,7,6] [.,[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]]=>[[[[[.,.],.],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[[.,.],.],[.,.]],[[.,.],[.,.]]]]=>[2,3,5,4,7,9,8,6,1] [[.,[[.,[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.]=>[1,3,2,5,7,8,6,4,9] [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,4,5,6,7,8,3,9,2] [.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],.]=>[.,[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]]=>[3,2,5,4,7,9,8,6,1] [[[[[[.,.],.],.],.],[[[.,.],.],.]],.]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5] [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4] [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9] [[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9] [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]=>[2,5,4,3,6,7,8,9,1] [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9] [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[2,3,4,5,6,8,7,1,9] [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9] [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]]=>[[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.]=>[6,5,4,3,2,8,7,1,9] [[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11] [[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]=>[2,1,8,7,9,6,5,4,3] [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1] [.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1] [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]]=>[5,4,3,2,1,6,8,9,7] [[.,[.,[.,[[[[[.,.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9] [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9] [[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]],.]=>[.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[7,6,5,4,3,2,8,9,1,10] [[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]],.]=>[.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10] [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]=>[[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[2,3,4,5,6,1,7,9,8] [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.]=>[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]]=>[[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[1,7,6,5,4,3,8,9,2] [[.,[[.,.],[.,.]]],[[.,[.,.]],[.,.]]]=>[[[.,.],[[.,.],.]],[[[.,.],[.,.]],.]]=>[[[[.,.],[[.,.],.]],[[.,.],[.,.]]],.]=>[1,3,4,2,6,8,7,5,9] [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3] [.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]=>[2,8,7,6,5,4,3,9,1] [.,[[[[.,.],[.,.]],[[.,.],[.,.]]],.]]=>[[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[3,5,4,7,9,8,6,2,1] [[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10] [[[[[[[.,.],.],.],.],[[.,.],.]],.],.]=>[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[1,4,3,9,8,7,6,5,2] [[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[6,5,4,3,2,1,8,9,7] [.,[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[[.,.],[.,.]]],.]=>[.,[[[.,.],[[.,.],.]],[[.,.],[.,.]]]]=>[2,4,5,3,7,9,8,6,1]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
Map
left rotate
Description
Return the result of left rotation applied to a binary tree.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
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.