Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0 [.,[.,.]]=>[2,1]=>0 [[.,.],.]=>[1,2]=>1 [.,[.,[.,.]]]=>[3,2,1]=>0 [.,[[.,.],.]]=>[2,3,1]=>0 [[.,.],[.,.]]=>[1,3,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>1 [[[.,.],.],.]=>[1,2,3]=>2 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>0 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>0 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>0 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>0 [.,[[[.,.],.],.]]=>[2,3,4,1]=>0 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>1 [[.,.],[[.,.],.]]=>[1,3,4,2]=>1 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>1 [[[.,.],.],[.,.]]=>[1,2,4,3]=>2 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>1 [[.,[[.,.],.]],.]=>[2,3,1,4]=>1 [[[.,.],[.,.]],.]=>[1,3,2,4]=>2 [[[.,[.,.]],.],.]=>[2,1,3,4]=>2 [[[[.,.],.],.],.]=>[1,2,3,4]=>3 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>0 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>0 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>0 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>0 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>0 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>0 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>1 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>1 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>1 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>1 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>1 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>1 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>2 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>2 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>1 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>1 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>2 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>2 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>3 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>1 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>1 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>1 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>2 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>2 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>3 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>2 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>2 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>3 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>3 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>4 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>0 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>0 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>0 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>0 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>0 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>0 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>0 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>0 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>0 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>0 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>0 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>0 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>0 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>0 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>0 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>0 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>0 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>0 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>0 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>0 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>0 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>0 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>0 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>0 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>0 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>0 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>0 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>0 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>0 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>0 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>0 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>0 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>0 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>0 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>0 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>0 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>0 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>0 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>0 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>0 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>0 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>0 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>1 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>1 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>1 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>1 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>1 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>1 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>1 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>1 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>1 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>1 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>1 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>1 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>1 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>1 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>1 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>1 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>1 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>1 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>1 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>2 [[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>2 [[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>2 [[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>2 [[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>2 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>1 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>1 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>1 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>1 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>2 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>2 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>2 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>2 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>3 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>3 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>1 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>1 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>1 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>1 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>1 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>2 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>2 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>2 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>3 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>2 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>2 [[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>3 [[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>3 [[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>4 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>1 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>1 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>1 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>1 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>1 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>1 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>1 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>1 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>1 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>1 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>1 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>1 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>1 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>1 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>2 [[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>2 [[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>2 [[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>2 [[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>2 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>2 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>2 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>3 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>3 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>2 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>2 [[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>3 [[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>3 [[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>4 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>2 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>2 [[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>2 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>2 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>2 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>3 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>3 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>3 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[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>2 [[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>2 [[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>3 [[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>3 [[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>2 [[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>2 [[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>2 [[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>3 [[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>3 [[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>3 [[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>3 [[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>4 [[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>4 [[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>1 [[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>1 [[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>1 [[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>2 [[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>2 [[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>2 [[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>2 [[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>3 [[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>3 [[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>2 [[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>2 [[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>3 [[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>3 [[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>4 [[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>2 [[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>2 [[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>3 [[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>3 [[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>3 [[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>4 [[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>3 [[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>3 [[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>4 [[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>4 [[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>5 [[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>1 [[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>1 [[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>1 [[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>1 [[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>1 [[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>1 [[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>1 [[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>1 [[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>1 [[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>1 [[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>1 [[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>1 [[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>1 [[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>1 [[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>1 [[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>1 [[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>1 [[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>1 [[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>1 [[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>1 [[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>1 [[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>1 [[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>2 [[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>2 [[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>2 [[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>2 [[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>2 [[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>3 [[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>3 [[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>2 [[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>2 [[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>3 [[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>3 [[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>3 [[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>3 [[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>4 [[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>4 [[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>2 [[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>2 [[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>3 [[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>3 [[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>3 [[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>4 [[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>3 [[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>3 [[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>4 [[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>4 [[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>5 [[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>2 [[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>2 [[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>2 [[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>2 [[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>2 [[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>2 [[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>2 [[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>2 [[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>3 [[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>3 [[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>3 [[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>3 [[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>4 [[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>4 [[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>3 [[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>3 [[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>4 [[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>4 [[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>5 [[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>3 [[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>3 [[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>3 [[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>3 [[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>4 [[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>4 [[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>4 [[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>5 [[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>4 [[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>4 [[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>5 [[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>5 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>6
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Description
The number of global ascents of a permutation.
The global ascents are the integers $i$ such that
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i < k \leq n: \pi(j) < \pi(k)\}.$$
Equivalently, by the pigeonhole principle,
$$C(\pi)=\{i\in [n-1] \mid \forall 1 \leq j \leq i: \pi(j) \leq i \}.$$
For $n > 1$ it can also be described as an occurrence of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
According to [2], this is also the cardinality of the connectivity set of a permutation. The permutation is connected, when the connectivity set is empty. This gives oeis:A003319.
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.