Identifier
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-2
[.,.]=>[1]=>[.,.] [.,[.,.]]=>[2,1]=>[[.,.],.] [[.,.],.]=>[1,2]=>[.,[.,.]] [.,[.,[.,.]]]=>[3,2,1]=>[[[.,.],.],.] [.,[[.,.],.]]=>[2,3,1]=>[[.,.],[.,.]] [[.,.],[.,.]]=>[3,1,2]=>[[.,[.,.]],.] [[.,[.,.]],.]=>[2,1,3]=>[[.,.],[.,.]] [[[.,.],.],.]=>[1,2,3]=>[.,[.,[.,.]]] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[[[[.,.],.],.],.] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[[[.,.],.],[.,.]] [.,[[.,.],[.,.]]]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[[[.,.],.],[.,.]] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [[.,.],[.,[.,.]]]=>[4,3,1,2]=>[[[.,[.,.]],.],.] [[.,.],[[.,.],.]]=>[3,4,1,2]=>[[.,[.,.]],[.,.]] [[.,[.,.]],[.,.]]=>[4,2,1,3]=>[[[.,.],[.,.]],.] [[[.,.],.],[.,.]]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[[.,.],[.,[.,.]]] [[[.,.],[.,.]],.]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [[[[.,.],.],.],.]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]] [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]] [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.] [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]] [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.] [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]] [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.] [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]] [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.] [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]] [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]] [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.] [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]] [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.] [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]] [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.] [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.] [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.] [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.] [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]] [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]] [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]] [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]] [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]] [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.] [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.] [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]] [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.] [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.] [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.] [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.] [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.] [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]] [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]] [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.] [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.] [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]] [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.] [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]] [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.] [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]] [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.] [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.] [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]] [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.] [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]] [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.] [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.] [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.] [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.] [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.] [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.] [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.] [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.] [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.] [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.] [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.] [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.] [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.] [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]] 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[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.] [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.] [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.] [.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]] [[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] [[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] [[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] [[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]] [[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]] [[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]] [[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]] [[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]] [[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] [[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] [[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.