Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-3
[.,.]=>[1]=>[1]=>[.,.]
[.,[.,.]]=>[2,1]=>[2,1]=>[[.,.],.]
[[.,.],.]=>[1,2]=>[1,2]=>[.,[.,.]]
[.,[.,[.,.]]]=>[3,2,1]=>[3,1,2]=>[[.,[.,.]],.]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,1,3,2]=>[[.,[[.,.],.]],.]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,1,3]=>[[[.,.],[.,.]],.]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],.]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,1,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],.]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[[.,[[[.,.],.],[.,.]]],.]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,2,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],.]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,2,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,2,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],.]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],.]]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,6,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
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[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
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.
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
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
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