Identifier
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ 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]=>[2,3,1]=>[[.,.],[.,.]]
[.,[[.,.],.]]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[[.,.],[.,.]]=>[3,1,2]=>[3,1,2]=>[[.,[.,.]],.]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[2,4,3,1]=>[[.,.],[[.,.],.]]
[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[3,4,2,1]=>[[[.,.],.],[.,.]]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[3,1,4,2]=>[[.,[.,.]],[.,.]]
[[.,.],[[.,.],.]]=>[3,4,1,2]=>[4,1,3,2]=>[[.,[[.,.],.]],.]
[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[2,4,1,3]=>[[.,.],[[.,.],.]]
[[[.,.],.],[.,.]]=>[4,1,2,3]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[[[.,.],[.,.]],.]=>[3,1,2,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]
[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]
[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]
[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[[[.,.],.],[[.,.],.]]
[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]
[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,[.,.]],[.,[.,.]]]
[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[[.,[.,.]],[[.,.],.]]
[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,[[.,.],.]],[.,.]]
[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]
[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]
[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,.],[[.,.],[.,.]]]
[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[[.,.],[[[.,.],.],.]]
[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,[.,[.,.]]],[.,.]]
[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]
[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,.],[.,[[.,.],.]]]
[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[[[.,.],.],[[.,.],.]]
[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,[.,.]],[[.,.],.]]
[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,.],[[.,[.,.]],.]]
[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]
[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]]
[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]]
[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,.],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[[[[.,[.,.]],.],.],.]=>[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]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]
[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]
[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]
[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[[.,.],[[.,.],[[.,.],.]]]
[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[[.,.],[[[.,.],.],[.,.]]]
[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]
[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[[.,.],[[[.,.],[.,.]],.]]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]
[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]
[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[[[.,.],.],[[.,.],[.,.]]]
[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]
[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]
[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[[[[.,.],.],.],[[.,.],.]]
[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[[[.,.],[.,.]],[[.,.],.]]
[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]
[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.]
[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]
[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]
[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]
[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]
[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,[[.,.],.]],[[.,.],.]]
[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[.,[[[.,.],.],.]],[.,.]]
[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]
[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]
[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.]
[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[[.,[[[.,.],.],[.,.]]],.]
[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]
[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]
[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[[.,.],[[[.,.],.],[.,.]]]
[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]
[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]
[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]
[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[[[.,.],.],[[.,.],[.,.]]]
[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]
[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]
[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[[.,.],[[.,.],[[.,.],.]]]
[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[[[.,.],.],[.,[[.,.],.]]]
[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[[[[.,.],.],.],[[.,.],.]]
[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[[[.,.],[.,.]],[[.,.],.]]
[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]
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[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
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[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
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[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
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[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
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[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
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[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]
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[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
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[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
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[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[8,6,7,3,2,4,1,5]=>[4,3,7,2,1,8,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[4,1,8,3,2,7,6,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[[[.,[[.,.],.]],.],[.,[[.,.],.]]]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[[[.,[[.,.],.]],.],[[.,.],[.,.]]]=>[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[3,8,2,1,4,6,7,5]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[[[[.,.],[.,.]],.],[.,[[.,.],.]]]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[7,6,8,3,1,2,4,5]=>[3,1,8,2,4,7,6,5]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[4,3,5,2,8,1,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[[.,[[[.,.],.],[.,.]]],[[.,.],.]]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[8,7,4,2,3,5,1,6]=>[5,4,2,7,3,1,8,6]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[[.,[[[.,.],[.,.]],.]],[[.,.],.]]=>[7,8,4,2,3,5,1,6]=>[5,4,2,8,3,1,7,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
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[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[5,1,4,8,3,2,7,6]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[5,1,7,3,4,2,8,6]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[5,1,8,3,4,2,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
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[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
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[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
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[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
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[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
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[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
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[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]=>[8,7,3,2,4,1,5,6]=>[4,3,7,2,1,5,8,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
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[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[9,8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>[[[[.,.],.],[.,[.,[.,[[.,.],.]]]]],.]
[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]=>[8,9,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,9,8,2,1]=>[[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>[[.,.],[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>[[.,.],[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[9,4,3,2,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[8,7,1,2,3,4,5,6,9]=>[7,1,2,3,4,5,8,6,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[[.,[.,[[[[[[.,.],.],.],.],.],.]]],.]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,10,2,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>[[.,.],[.,[.,[.,[[[.,.],[.,.]],.]]]]]
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.
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
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
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
Sorry, this map was not found in the database.