Identifier
Mp00016: Binary trees left-right symmetryBinary trees
Mp00018: Binary trees left border symmetryBinary trees
Mp00016: Binary trees left-right symmetry Binary trees
Images
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Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0010;cc-rep-2Cc0010;cc-rep-3
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[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] [[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] [[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] [[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.] [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.] [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.] [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.]=>[.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.]=>[.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.] [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.]=>[.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.] [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
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 $T_1, T_2, T_3$.