Identifier
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Images
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Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2
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[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]]=>[[[.,[[[[.,.],.],.],.]],.],[[.,.],.]]=>[[[.,[[.,.],.]],.],[[[[.,.],.],.],.]] [[.,[[[.,.],.],.]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[[[[[.,.],.],.],.],.]] [[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]=>[[.,[[.,.],.]],[[[[[[.,.],.],.],.],.],.]] [[[[.,[[.,[.,.]],.]],[[.,.],.]],.],.]=>[[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]]=>[[[[.,[[.,[.,.]],.]],[[.,.],.]],.],.] [.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]=>[.,[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]] [.,[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] [.,[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]]=>[.,[[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]] [[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]]=>[[[[[.,[.,.]],.],.],.],[.,[[.,.],.]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],[.,.]] [.,[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]]=>[.,[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]]=>[.,[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]] [.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]] [[[[.,.],[.,[.,[[.,.],.]]]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],[[.,.],.]],.] [[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],[[.,.],.]],.]=>[[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]],.] [.,[.,[[[[.,.],[[.,.],.]],[[.,.],.]],.]]]=>[.,[.,[[[[.,.],[[.,.],.]],[[.,.],.]],.]]]=>[.,[.,[[[[.,.],[[.,.],.]],[[.,.],.]],.]]] [[[[.,.],[.,[.,[[.,.],.]]]],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],[.,[.,[[.,.],.]]]],.]=>[[[[.,.],[.,[.,[[.,.],.]]]],[.,[.,[[.,.],.]]]],.] [.,[.,[[[[.,.],[.,[.,[[.,.],.]]]],[[.,.],.]],.]]]=>[.,[.,[[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]],.]]]=>[.,[.,[[[[.,.],[.,[.,[[.,.],.]]]],[[.,.],.]],.]]] [.,[.,[[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]],.]]]=>[.,[.,[[[[.,.],[.,[.,[[.,.],.]]]],[[.,.],.]],.]]]=>[.,[.,[[[[.,.],[[.,.],.]],[.,[.,[[.,.],.]]]],.]]] [[.,[.,[[.,.],.]]],[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[.,[[.,[.,[[.,.],.]]],[[.,.],.]]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[.,[[.,.],.]],[.,[[.,.],.]]]] [[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],[.,.]]=>[[[[.,[.,.]],.],[.,.]],[[.,.],[.,[.,.]]]]=>[[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],[.,.]] [[[[[[.,[[.,[.,.]],.]],[.,.]],.],.],.],.]=>[[[[[[.,.],.],.],.],[.,.]],[[.,.],[.,.]]]=>[[[[[[.,[[.,[.,.]],.]],[.,.]],.],.],.],.] [[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],[.,.]]=>[[.,[.,.]],[[[[[[[[.,.],.],.],.],.],.],.],.]] [[.,[.,[[[.,.],.],.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[[[.,.],.],.]] [[[[[.,.],.],.],[[.,.],.]],[.,[.,.]]]=>[[[[[.,[.,[.,.]]],[[.,.],.]],.],.],.]=>[[[[[.,.],.],.],[[.,.],.]],[.,[.,.]]] [[[[[[[.,.],[.,.]],.],.],.],.],[.,[.,.]]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,[.,.]]] [[.,.],[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]=>[[.,.],[.,[.,[.,[[.,[[.,.],.]],.]]]]] [[.,.],[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[[.,[.,[.,[[.,.],[[[.,.],.],.]]]]],.]=>[[.,.],[.,[.,[[.,[[[.,.],.],.]],.]]]] [[.,.],[.,[[.,[[[[.,.],.],.],.]],.]]]=>[[.,[.,[[.,.],[[[[.,.],.],.],.]]]],.]=>[[.,.],[.,[[.,[[[[.,.],.],.],.]],.]]] [[.,[.,[.,[[.,[.,[.,.]]],.]]]],[.,.]]=>[[.,[.,.]],[.,[.,[[.,.],[.,[.,.]]]]]]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],[.,.]] [[[[[.,.],[.,.]],.],.],[[[.,.],.],.]]=>[[[[[.,[[[.,.],.],.]],.],.],[.,.]],.]=>[[[[[.,.],[.,.]],.],.],[[[.,.],.],.]] [[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],[.,.]] [.,[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]]]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],[[.,.],.]]]=>[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]]] [[[.,[[.,.],[.,.]]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,[.,.]],.]] [.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]=>[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]] [.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]]=>[.,[[.,.],[[.,.],[[.,[[.,.],[.,.]]],.]]]]=>[.,[[.,[[.,[[.,.],[[.,[.,.]],.]]],.]],.]] [[[.,[[.,[[.,[.,.]],.]],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[.,[.,.]],[[.,.],[.,.]]]]=>[[[.,[[.,[[.,[.,.]],.]],[.,.]]],[.,.]],.] [[[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],[[.,.],.]]]=>[[[[.,[[.,[[.,.],.]],[.,.]]],[.,.]],[.,.]],[.,.]] [[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]]],[.,.]]=>[[.,[.,.]],[[.,[[.,[.,.]],[[.,.],.]]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[.,.]]]],[.,.]] [[.,[[.,[[.,.],.]],[.,.]]],[[.,[[.,.],.]],[.,.]]]=>[[.,[[.,[.,.]],[[.,.],.]]],[[.,[.,.]],[[.,.],.]]]=>[[.,[[.,[[.,.],.]],[.,.]]],[[.,[[.,.],.]],[.,.]]] [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,[.,.]],.]] [.,[[.,.],[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]]=>[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]],.]]=>[.,[[.,.],[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]] [.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]],.]]=>[.,[[.,.],[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]]]=>[.,[[.,[[[.,[[.,.],[.,.]]],.],[[.,[.,.]],.]]],.]] [[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]]=>[[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],[.,.]],.] [[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]=>[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.] [[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]=>[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]=>[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.] [.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]=>[.,[[.,[[.,[[.,[[[.,.],.],.]],.]],.]],.]] [[.,[[[.,.],[.,.]],.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[[[.,.],[.,.]],.]]=>[[.,[[[.,.],[.,.]],.]],[[[.,.],[.,.]],.]] [[[.,.],[.,.]],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]=>[[[.,[[[.,.],[.,[[[.,.],[.,.]],.]]],.]],[.,.]],.]=>[[[.,.],[.,.]],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]] [[[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]],.],.]=>[[[.,.],.],[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]=>[[[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]],.],.] [.,[.,[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]]]=>[.,[.,[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]]]=>[.,[.,[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]]] [[.,[[[[.,.],.],.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[[[.,.],.],.],.]]=>[[.,[[[[.,.],.],.],.]],[.,[[.,.],.]]] [[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]]=>[[.,[.,[[[.,.],.],.]]],[[[.,.],.],.]]=>[[.,[[[.,.],.],.]],[.,[[[.,.],.],.]]] [[.,[[[[[.,.],.],.],.],.]],[.,[[.,.],.]]]=>[[.,[.,[[.,.],.]]],[[[[[.,.],.],.],.],.]]=>[[.,[[[[[.,.],.],.],.],.]],[.,[[.,.],.]]] [[[.,[[[.,.],.],.]],.],[.,[[.,.],.]]]=>[[[.,[.,[[.,.],.]]],.],[[[.,.],.],.]]=>[[[.,[[[.,.],.],.]],.],[.,[[.,.],.]]] [[.,[[.,.],.]],[.,[[[[[.,.],.],.],.],.]]]=>[[.,[.,[[[[[.,.],.],.],.],.]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[[[[[.,.],.],.],.],.]]]
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 $T_1, T_2, T_3$.