Identifier
Mp00018: left border symmetryBinary trees
Mp00016: left-right symmetry
Images
=>
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 $T_1, T_2, T_3$.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.