edit this map or download as text // json
Identifier
Mp00018: Binary trees left border symmetry Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
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[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]] [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]] [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]] [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] [[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]],[.,.]] [[.,[.,.]],[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]]=>[[.,[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]],[.,.]] [[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]]=>[[.,[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]],[.,.]] [[.,[.,.]],[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]]=>[[.,[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]],[.,.]] [[.,[.,.]],[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]]=>[[.,[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]],[.,.]] 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[[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]],[.,.]] [[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[[.,.],[.,.]]]] [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[[.,.],[.,.]]]] [[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[.,[[.,.],[[.,.],[.,.]]]],[[[.,.],[.,.]],[.,.]]] [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]] [[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]],[.,.]] [[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]],[.,.]] [[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[[.,.],[.,.]]] [[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[[.,.],[.,.]]] [[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]]=>[[[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]],[.,.]] [[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]]=>[[[[.,[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]],[.,.]] [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[[.,.],[.,.]]]]] [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[.,.],[[[.,.],[.,.]],[.,.]]]] [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[[.,.],[.,.]]],[.,.]]] [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]] [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[.,[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]] [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]],[.,.]] [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]],[.,.]] [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]] [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]],[.,.]] [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[[.,.],[.,.]]]] [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[.,[[.,.],[.,.]]],[.,.]],[[[.,.],[.,.]],[.,.]]] [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]],[.,.]] [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[[.,.],[.,.]]] [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]]=>[[[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]],[.,.]] [[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] [[.,[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[.,.],[[[.,.],[.,.]],[.,.]]]]] [[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],[[.,.],[.,.]]],[.,.]]]] [[.,[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[[.,.],[.,.]]]]] [[.,[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[.,.],[[[[.,.],[.,.]],[.,.]],[.,.]]]] [[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[.,.],[[.,.],[.,.]]]],[.,.]]] [[.,[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[[.,.],[.,.]],[.,.]]],[.,.]]] [[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]] [[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],[[.,.],[.,.]]],[.,.]],[.,.]]] [[.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]] [[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]] [[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]] [[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]] [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] [[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]] [[[.,[.,.]],[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]],[.,.]] [[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]],[.,.]] [[[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]] [[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]] [[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]] [[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]] [[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]] [[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]],[.,.]] [[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] [[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[[.,[.,.]],[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]] [[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]],[.,.]] [[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[[.,.],[.,.]]] [[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[[.,[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] [[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] [[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[.,.],[[[.,.],[.,.]],[.,.]]]] [[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,.],[[.,.],[.,.]]],[.,.]]] [[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]] [[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[[[.,[.,.]],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]] [[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]],[.,.]] [[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]] [[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]] [[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]] [[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[[.,.],[.,.]]]] [[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[[[[.,[.,.]],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]] [[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]] [[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]
click to show experimental identities (only identities of compositions of up to three maps are shown)
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 $T_1, T_2, T_3$.
Properties
bijective, graded, involutive
Sage code
def mapping(elt):
    return elt.left_border_symmetry()
Weight
11
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey