Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0 [.,[.,.]]=>[2,1]=>0 [[.,.],.]=>[1,2]=>1 [.,[.,[.,.]]]=>[3,2,1]=>0 [.,[[.,.],.]]=>[2,3,1]=>0 [[.,.],[.,.]]=>[3,1,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>1 [[[.,.],.],.]=>[1,2,3]=>2 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>0 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>0 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>0 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>0 [.,[[[.,.],.],.]]=>[2,3,4,1]=>0 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>1 [[.,.],[[.,.],.]]=>[3,4,1,2]=>1 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>1 [[[.,.],.],[.,.]]=>[4,1,2,3]=>2 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>1 [[.,[[.,.],.]],.]=>[2,3,1,4]=>1 [[[.,.],[.,.]],.]=>[3,1,2,4]=>2 [[[.,[.,.]],.],.]=>[2,1,3,4]=>2 [[[[.,.],.],.],.]=>[1,2,3,4]=>3 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>0 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>0 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>0 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>0 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>0 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>0 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>0 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>0 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>0 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>0 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>0 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>0 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>0 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>0 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>1 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>1 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>1 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>1 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>1 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>1 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>2 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>2 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>2 [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>3 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>1 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>1 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>1 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>1 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>1 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>2 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>2 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>3 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>2 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>2 [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>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 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>0 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>0 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>0 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>0 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>0 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>0 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>0 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>0 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>0 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>0 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>0 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>0 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>0 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>0 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>0 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>0 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>0 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>0 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>0 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>0 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>0 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>0 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>0 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>0 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>0 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>0 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>0 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>0 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>0 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>0 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>0 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>0 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>0 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>0 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>0 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>0 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>0 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>0 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>0 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>0 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>1 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>1 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>1 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>1 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>1 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>1 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>1 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>1 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>1 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>1 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>1 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>1 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>1 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>1 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>1 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>1 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>2 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>2 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>2 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>1 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>1 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>2 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>2 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>3 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>3 [[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1 [[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>1 [[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1 [[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>1 [[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>1 [[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>2 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>2 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>2 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>3 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>2 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>2 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>3 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>3 [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>4 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>1 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>1 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>1 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>1 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>1 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>1 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>1 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>1 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>1 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>1 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>1 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>1 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>1 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>1 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>2 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>2 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>2 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>2 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>2 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>2 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>2 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>3 [[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>3 [[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>2 [[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>2 [[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>3 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>3 [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>4 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>2 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>2 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>2 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>2 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>2 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>3 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>3 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>3 [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>4 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>3 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>3 [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>4 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>4 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>5 [[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>6
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Description
The number of ascent tops in the permutation such that all smaller elements appear before.
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.