Identifier
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-3
[.,.]=>[1]=>[1]=>[.,.] [.,[.,.]]=>[2,1]=>[2,1]=>[[.,.],.] [[.,.],.]=>[1,2]=>[1,2]=>[.,[.,.]] [.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.] [.,[[.,.],.]]=>[2,3,1]=>[2,3,1]=>[[.,.],[.,.]] [[.,.],[.,.]]=>[1,3,2]=>[3,1,2]=>[[.,[.,.]],.] [[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.] [.,[.,[[.,.],.]]]=>[3,4,2,1]=>[3,4,2,1]=>[[[.,.],.],[.,.]] [.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.] [.,[[.,[.,.]],.]]=>[3,2,4,1]=>[3,2,4,1]=>[[[.,.],.],[.,.]] [.,[[[.,.],.],.]]=>[2,3,4,1]=>[2,3,4,1]=>[[.,.],[.,[.,.]]] [[.,.],[.,[.,.]]]=>[1,4,3,2]=>[4,3,1,2]=>[[[.,[.,.]],.],.] [[.,.],[[.,.],.]]=>[1,3,4,2]=>[3,1,4,2]=>[[.,[.,.]],[.,.]] [[.,[.,.]],[.,.]]=>[2,1,4,3]=>[4,2,1,3]=>[[[.,.],[.,.]],.] [[[.,.],.],[.,.]]=>[1,2,4,3]=>[4,1,2,3]=>[[.,[.,[.,.]]],.] [[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [[.,[[.,.],.]],.]=>[2,3,1,4]=>[2,3,1,4]=>[[.,.],[.,[.,.]]] [[[.,.],[.,.]],.]=>[1,3,2,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]] [[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]] [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]] [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.] [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]] [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]] [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.] [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[4,2,5,3,1]=>[[[.,.],[.,.]],[.,.]] [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.] [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.] [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]] [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]] [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]] [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]] [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]] [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.] [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]] [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[5,3,1,4,2]=>[[[.,[.,.]],[.,.]],.] [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[4,3,1,5,2]=>[[[.,[.,.]],.],[.,.]] [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[3,1,4,5,2]=>[[.,[.,.]],[.,[.,.]]] [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.] [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[4,2,1,5,3]=>[[[.,.],[.,.]],[.,.]] [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.] [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[4,1,2,5,3]=>[[.,[.,[.,.]]],[.,.]] [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.] [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.] [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.] [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.] [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.] [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]] [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]] [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]] [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]] [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]] [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]] [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]] [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]] [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]] [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.] [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]] [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.] [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.] [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>[[[.,.],[.,[.,.]]],[.,.]] [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.] [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.] [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.] [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.] [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]] [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]] [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]] [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]] [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]] [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]] [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]] [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]] [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.] [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]] [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.] [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]] [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>[[.,[[.,.],.]],[.,[.,.]]] [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],.] [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],.] [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],.] [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[.,.]] [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>[[.,[[.,.],.]],[.,[.,.]]] [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>[[[.,[.,.]],[.,.]],[.,.]] [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>[[[.,[.,.]],.],[.,[.,.]]] [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]] [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.] [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,.]] [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>[[[[.,.],[.,.]],[.,.]],.] [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>[[[.,.],[.,.]],[.,[.,.]]] [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.] [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]] [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],.] [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>[[[.,[.,[.,.]]],.],[.,.]] [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]] [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.] [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.] [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>[[[.,.],[.,[.,.]]],[.,.]] [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.] [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>[[[.,[.,.]],[.,.]],[.,.]] [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.] [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.] [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[.,.]] [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.] [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.] [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.] [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.] [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.] [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.] [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],.] [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.] [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.] [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.] [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.] [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.] [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.] [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]] [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]] [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]] [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]] [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>[[.,[[.,.],.]],[.,[.,.]]] [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[.,.]] [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>[[[.,[.,.]],.],[.,[.,.]]] [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]] [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]] [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]] [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]] [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]] [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]] [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]] [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]] [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]] [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]] [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]] [.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.] [.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]] [.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.] [.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.] [.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.] [.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.] [.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.] [.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.] [.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]] [.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]] [.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]] [.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]] [.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]] 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[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.] [.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.] [.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]] [.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.] 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[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.] [[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.] [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]] [[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>[[[[[.,[.,.]],[.,.]],.],.],.] [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>[[[[[.,[.,.]],.],[.,.]],.],.] [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>[[[[[.,[.,.]],.],.],[.,.]],.] [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.] [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.] [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.] [[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[.,.]] [[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[6,5,3,1,4,7,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[6,4,3,1,5,7,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.] [[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]] [[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>[[[[.,.],[[.,.],.]],[.,.]],.] [[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]] [[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>[[[[[.,.],[.,.]],[.,.]],.],.] [[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>[[[[[.,.],[.,.]],.],[.,.]],.] [[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.] [[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[6,4,2,1,5,7,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.] [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.] [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]] [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.] [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.] [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[6,4,1,2,5,7,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.] [[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],[.,.]] [[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>[[[[[.,.],.],[.,.]],[.,.]],.] [[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],.] [[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.] [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]] [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.] [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.] [[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]] [[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.] [[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.] [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]] [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.] [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.] [[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],.] [[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.] [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.] [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.] [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.] [[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.] [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.] [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.] [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.] [[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.] 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[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]] [[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]] [[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]] [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[5,3,1,4,6,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]] [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]] [[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]] [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]] [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]] [[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]] [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]] [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]] [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]] [[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]] [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]] [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]] [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]] [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]] [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]] [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]] [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]] [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]] [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[3,1,4,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]] [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]] [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]] [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]] [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]] [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]] [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]] [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]] [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]] [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]] [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 312-avoiding permutation
Description
Return a 312-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 minimal element of this Sylvester class.
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
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.