edit this map or download as text // json
Identifier
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
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[[.,[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.]],.]=>[.,[[.,[[.,[[[[.,.],[.,.]],[[.,.],.]],.]],.]],.]] [[.,[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[[[.,.],[.,.]],[[.,.],.]]],.]],.]] [[.,[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]],.]=>[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]],.]] [[.,[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]]],.]=>[.,[[[.,.],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]],.]] [[.,[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]],.]] [[[.,[.,.]],[[.,[[.,.],[.,.]]],.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,[[[.,.],[.,.]],.]],[[.,.],.]]] [[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],.]]] [[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]] [[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]] [[[.,[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]],.],[.,.]]=>[[.,.],[.,[[.,[[[[.,.],[.,.]],[[.,.],.]],.]],.]]] [[[.,[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],[[[.,.],[.,.]],[[.,.],.]]],.]]] [[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]]=>[[.,.],[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]] [[[[.,[[.,[.,.]],[[.,.],[.,.]]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[[.,.],[.,.]],[[.,.],.]],.]]]] [[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]] [[.,[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.]],.]=>[.,[[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]],.]] [[.,[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.]],.]=>[.,[[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]],.]] [[.,[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]],.]=>[.,[[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],.]],.]] [[.,[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]],.]] [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]],.]=>[.,[[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]],.]] [[.,[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]],.]=>[.,[[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[.,.]]],.]] [[.,[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]],.]=>[.,[[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]],.]] [[.,[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]],.]] [[.,[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]],.]] [[.,[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]]],.]=>[.,[[[.,.],[.,[[.,[[[.,.],[[.,.],.]],.]],.]]],.]] [[.,[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]]],.]=>[.,[[[.,.],[.,[[[.,.],[[.,.],[[.,.],.]]],.]]],.]] [[.,[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]],.]=>[.,[[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]],.]] [[.,[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[.,[[[.,.],[[.,.],.]],.]]]],.]] [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] [[[.,.],[.,.]],[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]]=>[[[.,[[.,[[[.,.],[.,.]],.]],.]],.],[[.,.],[.,.]]] [[[.,.],[.,.]],[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]]=>[[[.,[[[.,.],[[.,.],[.,.]]],.]],.],[[.,.],[.,.]]] [[[.,[.,.]],[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.]=>[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],[[.,.],.]]] [[[.,.],[.,.]],[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]]=>[[[[.,.],[.,[[[.,.],[.,.]],.]]],.],[[.,.],[.,.]]] [[[.,.],[.,.]],[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[[.,.],[.,.]]]],.],[[.,.],[.,.]]] [[[.,[[.,.],[.,.]]],.],[.,[[.,[[.,.],[.,.]]],.]]]=>[[[.,[[[.,.],[.,.]],.]],.],[.,[[[.,.],[.,.]],.]]] [[[.,[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[.,.]]],.],[.,[[[.,.],[.,.]],.]]] [[[[.,.],[.,.]],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]]=>[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[[.,.],[.,.]]]] [[[[.,.],[.,.]],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[[.,.],[.,.]]]] [[[.,[[.,[[.,.],[.,.]]],.]],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[[.,[[[.,.],[.,.]],.]],.]]] [[[.,[[[.,.],[.,.]],[.,.]]],.],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[.,[[[.,.],[[.,.],[.,.]]],.]]] [[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[[[.,.],[.,.]],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]] [[[[.,[[.,.],[.,.]]],.],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],[.,[[[.,.],[.,.]],.]]]] [[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],.],[[.,.],[[.,.],[[.,.],[.,.]]]]] [[[.,[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]],.],[.,.]]=>[[.,.],[.,[[.,[[.,[[[.,.],[[.,.],.]],.]],.]],.]]] [[[.,[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]],.],[.,.]]=>[[.,.],[.,[[.,[[[.,.],[[.,.],[[.,.],.]]],.]],.]]] [[[.,[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]],.],[.,.]]=>[[.,.],[.,[[[[[.,.],[.,.]],.],[[.,.],[.,.]]],.]]] [[[.,[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]]] [[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]] [[[[.,.],[.,.]],[.,[[.,[[.,.],[.,.]]],.]]],[.,.]]=>[[.,.],[[[.,[[[.,.],[.,.]],.]],.],[[.,.],[.,.]]]] [[[[.,.],[.,.]],[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[[.,.],[.,.]]],.],[[.,.],[.,.]]]] [[[[.,[[.,.],[.,.]]],.],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[.,[[[.,.],[.,.]],.]]]] [[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[.,.]],.],[[.,.],[[.,.],[.,.]]]]] [[[[.,[[.,[[.,[.,.]],[.,.]]],.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,[[[.,.],[[.,.],.]],.]],.]]]] [[[[.,[[[.,[.,.]],[.,.]],[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],[[.,.],[[.,.],.]]],.]]]] [[[[[.,.],[.,.]],[.,[[.,.],[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],[.,.]],.],[[.,.],[.,.]]]]] [[[[[.,[[.,[.,.]],[.,.]]],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[[[.,.],[[.,.],.]],.]]]]] [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
Return the left-right symmetrized tree of a binary tree.
Properties
bijective, graded, involutive
Sage code
def mapping(elt):
    return elt.left_right_symmetry()
Weight
11
Created
Jan 19, 2020 at 07:29 by FindStatCrew
Updated
Jan 19, 2020 at 07:29 by Martin Rubey