Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>1 [.,[.,.]]=>[2,1]=>1 [[.,.],.]=>[1,2]=>2 [.,[.,[.,.]]]=>[3,2,1]=>1 [.,[[.,.],.]]=>[2,3,1]=>2 [[.,.],[.,.]]=>[3,1,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>2 [[[.,.],.],.]=>[1,2,3]=>3 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>1 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>2 [.,[[.,.],[.,.]]]=>[4,2,3,1]=>1 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>2 [.,[[[.,.],.],.]]=>[2,3,4,1]=>3 [[.,.],[.,[.,.]]]=>[4,3,1,2]=>1 [[.,.],[[.,.],.]]=>[3,4,1,2]=>2 [[.,[.,.]],[.,.]]=>[4,2,1,3]=>1 [[[.,.],.],[.,.]]=>[4,1,2,3]=>1 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>2 [[.,[[.,.],.]],.]=>[2,3,1,4]=>3 [[[.,.],[.,.]],.]=>[3,1,2,4]=>2 [[[.,[.,.]],.],.]=>[2,1,3,4]=>3 [[[[.,.],.],.],.]=>[1,2,3,4]=>4 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>1 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>2 [.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>1 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>2 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>3 [.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>1 [.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>2 [.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>1 [.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>1 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>2 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>3 [.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>2 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>3 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>4 [[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>1 [[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2 [[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>1 [[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>2 [[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>3 [[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>1 [[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>2 [[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>1 [[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>2 [[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1 [[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1 [[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1 [[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>1 [[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>1 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>2 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>3 [[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>2 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>3 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>4 [[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>2 [[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>3 [[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>2 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>3 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>4 [[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>3 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>4 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>5 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>1 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>2 [.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>1 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>2 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>3 [.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>1 [.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>2 [.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>1 [.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>1 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>2 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>3 [.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>2 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>3 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>4 [.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>1 [.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>2 [.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>1 [.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>2 [.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>3 [.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>1 [.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2 [.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>1 [.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2 [.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>1 [.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>1 [.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>1 [.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>1 [.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>1 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>2 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>3 [.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>2 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>3 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>4 [.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>2 [.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>3 [.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>2 [.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>2 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>3 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>4 [.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>3 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>4 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>5 [[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>1 [[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>2 [[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>1 [[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2 [[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>3 [[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>1 [[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2 [[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>1 [[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>1 [[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>2 [[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>3 [[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>2 [[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>3 [[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>4 [[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>1 [[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2 [[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>1 [[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>2 [[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>3 [[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>1 [[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2 [[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>1 [[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>2 [[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>3 [[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>1 [[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>2 [[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>1 [[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>2 [[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>1 [[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>2 [[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>1 [[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>2 [[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>1 [[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>2 [[.,[.,[.,[.,.]]]],[.,.]]=>[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]=>1 [[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1 [[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1 [[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1 [[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>1 [[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>1 [[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1 [[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>1 [[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>1 [[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>2 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>3 [[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>2 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>3 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>4 [[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>2 [[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>3 [[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>2 [[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>2 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>3 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>4 [[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>3 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>4 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>5 [[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>2 [[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>3 [[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>2 [[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>3 [[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>4 [[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>2 [[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>3 [[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>2 [[[[.,.],.],[[.,.],.]],.]=>[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]=>2 [[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>2 [[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>2 [[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>3 [[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>4 [[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>3 [[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>4 [[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>5 [[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>3 [[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>4 [[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>3 [[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>3 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>4 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>5 [[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>4 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>5 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>6
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Description
The number of left-to-right-maxima of a permutation.
An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a left-to-right-maximum if there does not exist a $j < i$ such that $\sigma_j > \sigma_i$.
This is also the number of weak exceedences of a permutation that are not mid-points of a decreasing subsequence of length 3, see [1] for more on the later description.
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.