Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0 [.,[.,.]]=>[2,1]=>1 [[.,.],.]=>[1,2]=>0 [.,[.,[.,.]]]=>[3,2,1]=>3 [.,[[.,.],.]]=>[2,3,1]=>2 [[.,.],[.,.]]=>[1,3,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>1 [[[.,.],.],.]=>[1,2,3]=>0 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>6 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>5 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>4 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>4 [.,[[[.,.],.],.]]=>[2,3,4,1]=>3 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>3 [[.,.],[[.,.],.]]=>[1,3,4,2]=>2 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>2 [[[.,.],.],[.,.]]=>[1,2,4,3]=>1 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>3 [[.,[[.,.],.]],.]=>[2,3,1,4]=>2 [[[.,.],[.,.]],.]=>[1,3,2,4]=>1 [[[.,[.,.]],.],.]=>[2,1,3,4]=>1 [[[[.,.],.],.],.]=>[1,2,3,4]=>0 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>10 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>9 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>8 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>8 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>7 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>7 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>6 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>6 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>5 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>7 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>6 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>5 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>5 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>4 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>6 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>5 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>4 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>4 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>3 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>4 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>3 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>3 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>2 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>4 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>3 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>2 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>2 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>6 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>5 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>4 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>4 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>3 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>3 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>2 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>3 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>2 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>15 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>14 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>13 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>13 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>12 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>12 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>11 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>11 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>10 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>12 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>11 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>10 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>10 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>9 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>11 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>10 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>9 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>9 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>8 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>9 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>8 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>8 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>7 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>9 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>8 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>7 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>7 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>6 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>11 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>10 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>9 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>9 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>8 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>8 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>7 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>7 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>6 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>8 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>7 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>6 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>6 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>5 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>10 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>9 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>8 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>8 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>7 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>7 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>6 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>6 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>5 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>7 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>6 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>5 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>5 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>4 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>7 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>6 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>5 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>5 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>4 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>6 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>5 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>4 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>4 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>3 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>6 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>5 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>5 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>4 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>4 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>3 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>4 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>3 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>3 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>2 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>7 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>6 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>5 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>5 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>4 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>4 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>3 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>3 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>2 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>4 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>3 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>2 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>2 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>1 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>10 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>9 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>8 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>8 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>7 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>7 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>6 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>6 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>5 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>7 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>6 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>5 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>5 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>4 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>6 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>5 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>4 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>4 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>3 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>4 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>3 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>3 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>2 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>4 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>3 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>2 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>2 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>1 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>6 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>5 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>4 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>4 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>3 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>3 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>2 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>2 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>1 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>3 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>2 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>1 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>1 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>0 [[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>10 [[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>9 [[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>11 [[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>10 [[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>9 [[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>9 [[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>8 [[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>9 [[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>8 [[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>8 [[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>7 [[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>8 [[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>7 [[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>7 [[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>6 [[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>8 [[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>8 [[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>7 [[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>7 [[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>6 [[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>7 [[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>6 [[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>6 [[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>5 [[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>10 [[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>9 [[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>8 [[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>8 [[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>7 [[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>7 [[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>6 [[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>6 [[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>5 [[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>7 [[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>6 [[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>5 [[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>5 [[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>4 [[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>7 [[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>6 [[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>5 [[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>5 [[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>4 [[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>6 [[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>5 [[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>4 [[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>4 [[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>3 [[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>6 [[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>5 [[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>5 [[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>4 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>4 [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>3 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>4 [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>3 [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>3 [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>2 [[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>6 [[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>5 [[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>5 [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>4 [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>4 [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>3 [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>3 [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>2 [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>4 [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>3 [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>2 [[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>2 [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>1 [[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>8 [[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>7 [[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>7 [[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>6 [[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>6 [[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>5 [[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>6 [[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>5 [[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>5 [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>4 [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>6 [[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>5 [[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>4 [[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>4 [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>3 [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>4 [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>3 [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>3 [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>2 [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>4 [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>3 [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>2 [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>2 [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>1 [[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>5 [[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>4 [[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>4 [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>3 [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>3 [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>2 [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>2 [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>1 [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>3 [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>2 [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>1 [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>1 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>0
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Description
The number of transpositions that are smaller or equal to a permutation in Bruhat order.
A statistic is known to be smooth if and only if this number coincides with the number of inversions. This is also equivalent for a permutation to avoid the two pattern $4231$ and $3412$.
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.