Identifier
Mp00029:
Dyck paths
—to binary tree: left tree, up step, right tree, down step⟶
Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2Cc0021;cc-rep-3
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[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[[[],[]],[[[[],[[],[]]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[[],[]],[]]]],[[],[]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[],[]],[[[],[[],[]]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[[],[]],[]]],[[],[]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[[[],[]],[[[],[[],[]]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[[],[]],[]]],[[],[]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]=>[[[[],[]],[[],[[[],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[]]],[]],[[],[]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[[[[],[]],[[[],[[[],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[]]],[]]],[[],[]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[[[],[]],[[[[[],[[],[[],[]]]],[]],[]],[]]]=>[[[],[[],[[],[[[[],[]],[]],[]]]]],[[],[]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[[[],[]],[[[[],[[],[[],[]]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[[],[]],[]],[]]]],[[],[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]=>[[[],[]],[[[[],[[],[[],[]]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[[],[]],[]],[]]]],[[],[]]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[[[],[]],[[[],[[],[[],[]]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[[],[]],[]],[]]],[[],[]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]=>[[[],[]],[[[],[[],[[],[]]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[[],[]],[]],[]]],[[],[]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[[],[[],[]]],[]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[],[[[],[]],[]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[[[],[[],[]]],[]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[],[[[],[]],[]]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[[[[],[[],[]]],[]],[[[[],[[],[]]],[]],[]]]=>[[[],[[],[[[],[]],[]]]],[[],[[[],[]],[]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]=>[[[[],[[],[]]],[]],[[[],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[]]],[[],[[[],[]],[]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[[[],[[],[]]],[[],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[]],[[[],[]],[]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[[[[],[[],[]]],[[],[]]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[[],[]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[[[[],[[],[]]],[[],[]]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[[],[]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[],[[],[]]],[[],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[[[[],[[],[]]],[[[],[]],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[[],[]]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]=>[[[[],[[],[]]],[[[],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[]]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[[[[],[[],[]]],[[[],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[]]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[[[],[[],[]]],[[[[],[]],[[],[]]],[[],[]]]]=>[[[[],[]],[[[],[]],[[],[]]]],[[[],[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[[[[],[[],[]]],[[[],[]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[],[]]],[[[],[]],[]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[[[],[[],[]]],[[[[],[]],[[[],[]],[]]],[]]]=>[[[],[[[],[[],[]]],[[],[]]]],[[[],[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]=>[[[],[[],[]]],[[[],[]],[[[[],[]],[]],[]]]]=>[[[[],[[],[[],[]]]],[[],[]]],[[[],[]],[]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[[[],[[],[]]],[[[],[]],[[[],[]],[[],[]]]]]=>[[[[[],[]],[[],[]]],[[],[]]],[[[],[]],[]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[[[],[[],[]]],[[[],[]],[[],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[]],[[],[]]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[[[[],[[],[]]],[[],[[],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[]],[]],[[[],[]],[]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[[],[[],[]]],[[],[[],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[]],[]],[[[],[]],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[[],[]]],[[[],[[],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[[[[],[[],[]]],[[[[],[[],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[]],[]]]],[[[],[]],[]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[[[],[[],[]]],[[[[[],[[],[]]],[]],[]],[]]]=>[[[],[[],[[],[[[],[]],[]]]]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[[[],[[],[]]],[[[[],[[],[]]],[]],[[],[]]]]=>[[[[],[]],[[],[[[],[]],[]]]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[[[[],[[],[]]],[[[],[[],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[]],[]]],[[[],[]],[]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[],[[],[]]],[[[[],[[],[]]],[[],[]]],[]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[],[[],[]]],[[[],[[],[]]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[[],[]],[]]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]=>[[[],[[],[]]],[[[],[[],[]]],[[],[[],[]]]]]=>[[[[[],[]],[]],[[[],[]],[]]],[[[],[]],[]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[[[],[[],[]]],[[],[[[],[]],[[[],[]],[]]]]]=>[[[[[],[[],[]]],[[],[]]],[]],[[[],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[[[],[[],[]]],[[],[[[[],[[],[]]],[]],[]]]]=>[[[[],[[],[[[],[]],[]]]],[]],[[[],[]],[]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[[[],[[],[]]],[[],[[[],[[],[]]],[[],[]]]]]=>[[[[[],[]],[[[],[]],[]]],[]],[[[],[]],[]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]=>[[[[[],[[[],[]],[]]],[]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[],[[[],[[],[]]],[]]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[[[[],[[[],[]],[]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[],[[],[]]],[]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[[[[],[[[],[]],[]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[],[[],[]]],[]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[[[[],[[[],[]],[]]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[[],[[],[]]],[]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[[[[],[[[],[]],[]]],[[],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[]],[[[],[[],[]]],[]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[[[[],[[[[],[]],[]],[]]],[]],[[],[[],[]]]]=>[[[[],[]],[]],[[],[[[],[[],[[],[]]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[[[[],[[[[],[]],[]],[]]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[[],[[],[[],[]]]],[]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[[[],[[[[],[]],[]],[]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[],[[],[[],[]]]],[]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[[[],[[[[[],[]],[]],[]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[],[[],[[],[]]]]],[]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]=>[[[],[[[[[],[]],[]],[]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[],[[],[[],[]]]]],[]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[[[],[[[[[],[]],[]],[]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[],[[],[[],[]]]]],[]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[[[[],[[[[],[]],[]],[[],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[]],[[],[[],[]]]],[]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[[[],[[[],[]],[[],[]]]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[[[],[]],[[],[]]],[]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[[[],[[[[],[]],[[],[]]],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[[[],[]],[[],[]]]],[]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[[[],[[[[],[]],[[],[]]],[[],[]]]],[[],[]]]=>[[[],[]],[[[[],[]],[[[],[]],[[],[]]]],[]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[[[],[[[[],[]],[[],[]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[],[]],[[],[]]]],[]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[[[],[[[],[]],[[[],[]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[],[]]],[[],[]]],[]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[[[],[[[[],[]],[[[],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[]]],[[],[]]]],[]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[[[],[[[[],[]],[[[],[]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[],[]]],[[],[]]]],[]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[[[[[],[[],[[],[]]]],[]],[]],[[[],[]],[]]]=>[[[],[[],[]]],[[],[[],[[[[],[]],[]],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[[[[],[[],[[],[]]]],[]],[[],[]]],[[],[]]]=>[[[],[]],[[[],[]],[[],[[[[],[]],[]],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[[[[[],[[],[[],[]]]],[]],[[[],[]],[]]],[]]=>[[],[[[],[[],[]]],[[],[[[[],[]],[]],[]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[[[[],[[],[[],[]]]],[]],[[[[],[]],[]],[]]]=>[[[],[[],[[],[]]]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]=>[[[[],[[],[[],[]]]],[]],[[[],[]],[[],[]]]]=>[[[[],[]],[[],[]]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[[[[],[[],[[],[]]]],[]],[[],[[[],[]],[]]]]=>[[[[],[[],[]]],[]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[],[[],[[],[]]]],[]],[[],[[],[[],[]]]]]=>[[[[[],[]],[]],[]],[[],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[[[[],[[],[[],[]]]],[[],[]]],[]],[[],[]]]=>[[[],[]],[[],[[[],[]],[[[[],[]],[]],[]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[[[[[],[[],[[],[]]]],[[],[]]],[[],[]]],[]]=>[[],[[[],[]],[[[],[]],[[[[],[]],[]],[]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[[[.,[.,[.,.]]],[.,.]],[[.,.],.]]=>[[[[],[[],[[],[]]]],[[],[]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[[],[[],[[],[]]]],[[],[]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[],[]],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[[[[[],[[],[[],[]]]],[[[],[]],[]]],[]],[]]=>[[],[[],[[[],[[],[]]],[[[[],[]],[]],[]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]=>[[[[],[[],[[],[]]]],[[[],[]],[]]],[[],[]]]=>[[[],[]],[[[],[[],[]]],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[],[[],[[],[]]]],[[[[],[]],[]],[]]],[]]=>[[],[[[],[[],[[],[]]]],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[[[],[[],[[],[]]]],[[[[[],[]],[]],[]],[]]]=>[[[],[[],[[],[[],[]]]]],[[[[],[]],[]],[]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[[[],[[],[[],[]]]],[[[[],[]],[]],[[],[]]]]=>[[[[],[]],[[],[[],[]]]],[[[[],[]],[]],[]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]=>[[[[],[[],[[],[]]]],[[[],[]],[[],[]]]],[]]=>[[],[[[[],[]],[[],[]]],[[[[],[]],[]],[]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[[[],[[],[[],[]]]],[[[[],[]],[[],[]]],[]]]=>[[[],[[[],[]],[[],[]]]],[[[[],[]],[]],[]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[[[],[[],[[],[]]]],[[[],[]],[[[],[]],[]]]]=>[[[[],[[],[]]],[[],[]]],[[[[],[]],[]],[]]]
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[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]=>[[[],[[[],[[[[],[]],[]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[],[[],[]]]],[]]],[]]]
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[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]=>[[[],[[[],[[],[[],[]]]],[[[],[]],[]]]],[]]=>[[],[[[[],[[],[]]],[[[[],[]],[]],[]]],[]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[[[],[[[],[[],[[],[]]]],[[],[[],[]]]]],[]]=>[[],[[[[[],[]],[]],[[[[],[]],[]],[]]],[]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]=>[[[[[],[[],[[[],[[],[]]],[]]]],[]],[]],[]]=>[[],[[],[[],[[[[],[[[],[]],[]]],[]],[]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[[[.,[.,[[.,[.,.]],.]]],.],[.,.]]=>[[[[],[[],[[[],[[],[]]],[]]]],[]],[[],[]]]=>[[[],[]],[[],[[[[],[[[],[]],[]]],[]],[]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[[[[],[[],[[[],[[],[]]],[]]]],[[],[]]],[]]=>[[],[[[],[]],[[[[],[[[],[]],[]]],[]],[]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]=>[[[],[[],[[[],[[],[]]],[]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[],[[[],[]],[]]],[]],[]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[[[],[[],[[[],[[],[]]],[]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[],[[[],[]],[]]],[]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[[[[],[[[],[[[],[[],[]]],[]]],[]]],[]],[]]=>[[],[[],[[[],[[[],[[[],[]],[]]],[]]],[]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[],[[[],[[[],[[],[]]],[]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[[.,[.,.]],.]],.],.]],.]=>[[[],[[[[],[[[],[[],[]]],[]]],[]],[]]],[]]=>[[],[[[],[[],[[[],[[[],[]],[]]],[]]]],[]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[[[],[[[],[[[],[[],[]]],[]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[],[[[],[]],[]]],[]]],[]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]=>[[[[],[[],[[[[],[[],[]]],[]],[]]]],[]],[]]=>[[],[[],[[[[],[[],[[[],[]],[]]]],[]],[]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[[[],[[],[[[[],[[],[]]],[]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[],[[[],[]],[]]]],[]],[]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[[.,[.,.]],.],.]],.]],.]=>[[[],[[[],[[[[],[[],[]]],[]],[]]],[]]],[]]=>[[],[[[],[[[],[[],[[[],[]],[]]]],[]]],[]]]
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[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[[.,[.,[.,[[.,.],.]]]],[[.,.],.]]=>[[[],[[],[[],[[[],[]],[]]]]],[[[],[]],[]]]=>[[[],[[],[]]],[[[[[],[[],[]]],[]],[]],[]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[[[],[[],[[],[[[],[]],[]]]]],[[],[[],[]]]]=>[[[[],[]],[]],[[[[[],[[],[]]],[]],[]],[]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[[[[],[[[],[[],[[[],[]],[]]]],[]]],[]],[]]=>[[],[[],[[[],[[[[],[[],[]]],[]],[]]],[]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]=>[[[],[[[],[[],[[[],[]],[]]]],[]]],[[],[]]]=>[[[],[]],[[[],[[[[],[[],[]]],[]],[]]],[]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[[.,[[[.,[.,[[.,.],.]]],.],.]],.]=>[[[],[[[[],[[],[[[],[]],[]]]],[]],[]]],[]]=>[[],[[[],[[],[[[[],[[],[]]],[]],[]]]],[]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]=>[[[],[[[],[[],[[[],[]],[]]]],[[],[]]]],[]]=>[[],[[[[],[]],[[[[],[[],[]]],[]],[]]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[[[.,[.,[[.,[[.,.],.]],.]]],.],.]=>[[[[],[[],[[[],[[[],[]],[]]],[]]]],[]],[]]=>[[],[[],[[[[],[[[],[[],[]]],[]]],[]],[]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[[[],[[],[[[],[[[],[]],[]]],[]]]],[[],[]]]=>[[[],[]],[[[[],[[[],[[],[]]],[]]],[]],[]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[[[],[[[],[[[],[[[],[]],[]]],[]]],[]]],[]]=>[[],[[[],[[[],[[[],[[],[]]],[]]],[]]],[]]]
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to complete tree
Description
Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
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