Identifier
Mp00018: left border symmetryBinary trees
Mp00017: to 312-avoiding permutationPermutations
Mp00059: Permutations Robinson-Schensted insertion tableau
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0007;cc-rep-3
[.,.]=>[.,.]=>[1]=>[[1]] [.,[.,.]]=>[.,[.,.]]=>[2,1]=>[[1],[2]] [[.,.],.]=>[[.,.],.]=>[1,2]=>[[1,2]] [.,[.,[.,.]]]=>[.,[.,[.,.]]]=>[3,2,1]=>[[1],[2],[3]] [.,[[.,.],.]]=>[.,[[.,.],.]]=>[2,3,1]=>[[1,3],[2]] [[.,.],[.,.]]=>[[.,[.,.]],.]=>[2,1,3]=>[[1,3],[2]] [[.,[.,.]],.]=>[[.,.],[.,.]]=>[1,3,2]=>[[1,2],[3]] [[[.,.],.],.]=>[[[.,.],.],.]=>[1,2,3]=>[[1,2,3]] [.,[.,[.,[.,.]]]]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[[1],[2],[3],[4]] [.,[.,[[.,.],.]]]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[[1,4],[2],[3]] [.,[[.,.],[.,.]]]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[[1,4],[2],[3]] [.,[[.,[.,.]],.]]=>[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[[1,3],[2],[4]] [.,[[[.,.],.],.]]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[[1,3,4],[2]] [[.,.],[.,[.,.]]]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[[1,4],[2],[3]] [[.,.],[[.,.],.]]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[[1,3,4],[2]] [[.,[.,.]],[.,.]]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[[1,3],[2,4]] [[[.,.],.],[.,.]]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[[1,3,4],[2]] [[.,[.,[.,.]]],.]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[[1,2],[3],[4]] [[.,[[.,.],.]],.]=>[[.,.],[[.,.],.]]=>[1,3,4,2]=>[[1,2,4],[3]] [[[.,.],[.,.]],.]=>[[[.,.],[.,.]],.]=>[1,3,2,4]=>[[1,2,4],[3]] [[[.,[.,.]],.],.]=>[[[.,.],.],[.,.]]=>[1,2,4,3]=>[[1,2,3],[4]] [[[[.,.],.],.],.]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[[1,2,3,4]] [.,[.,[.,[.,[.,.]]]]]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[[1],[2],[3],[4],[5]] [.,[.,[.,[[.,.],.]]]]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[[1,5],[2],[3],[4]] [.,[.,[[.,.],[.,.]]]]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[[1,5],[2],[3],[4]] [.,[.,[[.,[.,.]],.]]]=>[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[[1,4],[2],[3],[5]] [.,[.,[[[.,.],.],.]]]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[[1,4,5],[2],[3]] [.,[[.,.],[.,[.,.]]]]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[[1,5],[2],[3],[4]] [.,[[.,.],[[.,.],.]]]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[[1,4,5],[2],[3]] [.,[[.,[.,.]],[.,.]]]=>[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[[1,4],[2,5],[3]] [.,[[[.,.],.],[.,.]]]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[[1,4,5],[2],[3]] [.,[[.,[.,[.,.]]],.]]=>[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[[1,3],[2],[4],[5]] [.,[[.,[[.,.],.]],.]]=>[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[[1,3,5],[2],[4]] [.,[[[.,.],[.,.]],.]]=>[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[[1,3,5],[2],[4]] [.,[[[.,[.,.]],.],.]]=>[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[[1,3,4],[2],[5]] [.,[[[[.,.],.],.],.]]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[[1,3,4,5],[2]] [[.,.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[[1,5],[2],[3],[4]] [[.,.],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[[1,4,5],[2],[3]] [[.,.],[[.,.],[.,.]]]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[[1,4,5],[2],[3]] [[.,.],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[[1,3,5],[2],[4]] [[.,.],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[[1,3,4,5],[2]] [[.,[.,.]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[[1,4],[2,5],[3]] [[.,[.,.]],[[.,.],.]]=>[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[[1,3,4],[2,5]] [[[.,.],.],[.,[.,.]]]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[[1,4,5],[2],[3]] [[[.,.],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[[1,3,4,5],[2]] [[.,[.,[.,.]]],[.,.]]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[[1,3],[2,4],[5]] [[.,[[.,.],.]],[.,.]]=>[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[[1,3,5],[2,4]] [[[.,.],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[[1,3,5],[2,4]] [[[.,[.,.]],.],[.,.]]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[[1,3,4],[2,5]] [[[[.,.],.],.],[.,.]]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[[1,3,4,5],[2]] [[.,[.,[.,[.,.]]]],.]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[[1,2],[3],[4],[5]] [[.,[.,[[.,.],.]]],.]=>[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[[1,2,5],[3],[4]] [[.,[[.,.],[.,.]]],.]=>[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[[1,2,5],[3],[4]] [[.,[[.,[.,.]],.]],.]=>[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[[1,2,4],[3],[5]] [[.,[[[.,.],.],.]],.]=>[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[[1,2,4,5],[3]] [[[.,.],[.,[.,.]]],.]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[[1,2,5],[3],[4]] [[[.,.],[[.,.],.]],.]=>[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[[1,2,4,5],[3]] [[[.,[.,.]],[.,.]],.]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[[1,2,4],[3,5]] [[[[.,.],.],[.,.]],.]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[[1,2,4,5],[3]] [[[.,[.,[.,.]]],.],.]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[[1,2,3],[4],[5]] [[[.,[[.,.],.]],.],.]=>[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[[1,2,3,5],[4]] [[[[.,.],[.,.]],.],.]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[[1,2,3,5],[4]] [[[[.,[.,.]],.],.],.]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[[1,2,3,4],[5]] [[[[[.,.],.],.],.],.]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[[1,2,3,4,5]] [.,[.,[.,[.,[.,[.,.]]]]]]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[[1],[2],[3],[4],[5],[6]] [.,[.,[.,[.,[[.,.],.]]]]]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[[1,6],[2],[3],[4],[5]] [.,[.,[.,[[.,.],[.,.]]]]]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[[1,6],[2],[3],[4],[5]] [.,[.,[.,[[.,[.,.]],.]]]]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[[1,5],[2],[3],[4],[6]] [.,[.,[.,[[[.,.],.],.]]]]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[[1,5,6],[2],[3],[4]] [.,[.,[[.,.],[.,[.,.]]]]]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[[1,6],[2],[3],[4],[5]] [.,[.,[[.,.],[[.,.],.]]]]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[[1,5,6],[2],[3],[4]] [.,[.,[[.,[.,.]],[.,.]]]]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[[1,5],[2,6],[3],[4]] [.,[.,[[[.,.],.],[.,.]]]]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[[1,5,6],[2],[3],[4]] [.,[.,[[.,[.,[.,.]]],.]]]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[[1,4],[2],[3],[5],[6]] [.,[.,[[.,[[.,.],.]],.]]]=>[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[[1,4,6],[2],[3],[5]] [.,[.,[[[.,.],[.,.]],.]]]=>[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[[1,4,6],[2],[3],[5]] [.,[.,[[[.,[.,.]],.],.]]]=>[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[[1,4,5],[2],[3],[6]] [.,[.,[[[[.,.],.],.],.]]]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[[1,4,5,6],[2],[3]] [.,[[.,.],[.,[.,[.,.]]]]]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[[1,6],[2],[3],[4],[5]] 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[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]] [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]=>[[1,2,3,4,5,6,7,8,10],[9]] [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]=>[[1,2,3,4,5,6,7,9,10],[8]] [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]=>[[1,2,3,4,5,6,8,9,10],[7]] [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]=>[[1,2,3,4,5,7,8,9,10],[6]] [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]=>[[1,2,3,4,6,7,8,9,10],[5]] [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]=>[[1,2,3,5,6,7,8,9,10],[4]] [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]=>[[1,2,4,5,6,7,8,9,10],[3]] [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[3,2,4,5,6,7,8,1,9]=>[[1,4,5,6,7,8,9],[2],[3]] [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[2,3,9,8,7,6,5,4,1]=>[[1,3,4],[2],[5],[6],[7],[8],[9]] [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]=>[[1,3,9],[2,4],[5],[6],[7],[8]] [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,3,1,9,8,7,6,5,4]=>[[1,3,4],[2,5],[6],[7],[8],[9]] [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]=>[[1,2,3,4,5,6,7,8,9,10,11]] [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]=>[[1,2,8],[3,9],[4],[5],[6],[7]] [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]=>[6,7,8,5,4,3,2,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]=>[7,8,9,6,5,4,3,2,1,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.]=>[6,7,5,8,4,3,2,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,7,1,9,8]=>[[1,3,4,5,6,7,8],[2,9]] [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[1,3,4,5,6,7,8,2,9]=>[[1,2,4,5,6,7,8,9],[3]] [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[6,7,5,4,3,2,1,9,8]=>[[1,7,8],[2,9],[3],[4],[5],[6]] [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]] [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[[1,5,6,7,8,9],[2],[3],[4]] [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[[1,6,7,8,9],[2],[3],[4],[5]] [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]] [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[[1,5,6,7,8,9,10],[2],[3],[4]] [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]] [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[[1,7,8,9,10],[2],[3],[4],[5],[6]] [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]=>[7,6,5,8,4,3,2,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[7,6,5,4,3,2,8,1,9]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.]=>[8,7,6,5,4,3,2,9,1,10]=>[[1,9,10],[2],[3],[4],[5],[6],[7],[8]] [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10]] [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[2,8,9,7,6,5,4,3,1]=>[[1,3,9],[2],[4],[5],[6],[7],[8]] [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[2,8,7,9,6,5,4,3,1]=>[[1,3,9],[2],[4],[5],[6],[7],[8]] [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]=>[[1,2,3,4,5,6,7,8,9,11],[10]] [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]=>[4,5,3,2,1,9,8,7,6]=>[[1,5,6],[2,7],[3,8],[4,9]] [[[[[[[.,.],.],.],.],.],[[.,.],.]],.]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[1,3,4,2,5,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]] [[[[[[.,.],.],.],.],[[[.,.],.],.]],.]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[1,3,4,5,2,6,7,8,9]=>[[1,2,4,5,6,7,8,9],[3]] [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]=>[[1,2,5,6,7,8,9],[3],[4]] [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]=>[1,3,4,5,6,7,9,8,2]=>[[1,2,4,5,6,7,8],[3],[9]] [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[7,6,5,4,3,2,8,9,1]=>[[1,8,9],[2],[3],[4],[5],[6],[7]] [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]=>[2,8,7,6,5,4,3,1,9]=>[[1,3,9],[2],[4],[5],[6],[7],[8]] [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[2,1,4,5,6,7,8,9,3]=>[[1,3,5,6,7,8,9],[2,4]] [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.]=>[[.,.],[[.,[[[[[.,.],.],.],.],.]],.]]=>[1,4,5,6,7,8,3,9,2]=>[[1,2,5,6,7,8,9],[3],[4]] [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]=>[[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[1,3,4,5,6,7,8,9,10,11],[2]] [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[4,3,2,5,6,7,8,9,1]=>[[1,5,6,7,8,9],[2],[3],[4]] [.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]=>[.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[5,4,3,2,6,7,8,9,1]=>[[1,6,7,8,9],[2],[3],[4],[5]] [[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]=>[[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.]=>[5,6,4,3,2,1,7,8,9,10]=>[[1,6,7,8,9,10],[2],[3],[4],[5]] [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]]=>[[[.,[.,.]],.],[[[[[.,.],.],.],.],.]]=>[2,1,3,5,6,7,8,9,4]=>[[1,3,4,6,7,8,9],[2,5]] [[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.]=>[6,5,7,8,4,3,2,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[.,.],[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.]=>[6,5,4,7,8,3,2,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[.,.],[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.]=>[6,5,4,3,2,7,8,1,9]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.]=>[7,6,8,9,5,4,3,2,1,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [[.,.],[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.]=>[7,6,5,8,9,4,3,2,1,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [[.,.],[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.]=>[7,6,5,4,3,8,9,2,1,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [[.,.],[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.]=>[7,6,5,4,3,2,8,9,1,10]=>[[1,8,9,10],[2],[3],[4],[5],[6],[7]] [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]=>[3,4,2,1,9,8,7,6,5]=>[[1,4,5],[2,6],[3,7],[8],[9]] [[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[1,9,8,10,7,6,5,4,3,2]=>[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]=>[10,9,11,8,7,6,5,4,3,2,1]=>[[1,11],[2],[3],[4],[5],[6],[7],[8],[9],[10]] [[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]=>[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]] [[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]=>[[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9,10]=>[[1,4,5,6,7,8,9,10],[2],[3]] [[[[[[.,.],.],.],.],[[.,.],.]],[.,.]]=>[[[[[[.,[.,.]],[[.,.],.]],.],.],.],.]=>[2,1,4,5,3,6,7,8,9]=>[[1,3,5,6,7,8,9],[2,4]] [[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]=>[[[[[.,[[.,[[.,.],.]],.]],.],.],.],.]=>[3,4,2,5,1,6,7,8,9]=>[[1,4,5,6,7,8,9],[2],[3]] [[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]=>[[[[[[.,[[.,.],.]],[.,.]],.],.],.],.]=>[2,3,1,5,4,6,7,8,9]=>[[1,3,4,6,7,8,9],[2,5]] [[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]=>[[1,2,4,6,7,8,9],[3,5]] [[[[[[[.,.],.],.],.],[[.,.],.]],.],.]=>[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]=>[1,2,4,5,3,6,7,8,9]=>[[1,2,3,5,6,7,8,9],[4]] [.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]=>[.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[6,5,4,3,2,7,8,9,1]=>[[1,7,8,9],[2],[3],[4],[5],[6]] [[[.,[[[.,.],.],[[[.,.],.],.]]],.],.]=>[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]]=>[1,2,5,6,7,4,8,9,3]=>[[1,2,3,6,7,8,9],[4],[5]]
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
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.