Identifier
Values
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>0 [.,[.,.]]=>[2,1]=>1 [[.,.],.]=>[1,2]=>0 [.,[.,[.,.]]]=>[3,2,1]=>2 [.,[[.,.],.]]=>[2,3,1]=>1 [[.,.],[.,.]]=>[1,3,2]=>1 [[.,[.,.]],.]=>[2,1,3]=>1 [[[.,.],.],.]=>[1,2,3]=>0 [.,[.,[.,[.,.]]]]=>[4,3,2,1]=>3 [.,[.,[[.,.],.]]]=>[3,4,2,1]=>2 [.,[[.,.],[.,.]]]=>[2,4,3,1]=>2 [.,[[.,[.,.]],.]]=>[3,2,4,1]=>2 [.,[[[.,.],.],.]]=>[2,3,4,1]=>1 [[.,.],[.,[.,.]]]=>[1,4,3,2]=>2 [[.,.],[[.,.],.]]=>[1,3,4,2]=>1 [[.,[.,.]],[.,.]]=>[2,1,4,3]=>2 [[[.,.],.],[.,.]]=>[1,2,4,3]=>1 [[.,[.,[.,.]]],.]=>[3,2,1,4]=>2 [[.,[[.,.],.]],.]=>[2,3,1,4]=>1 [[[.,.],[.,.]],.]=>[1,3,2,4]=>1 [[[.,[.,.]],.],.]=>[2,1,3,4]=>1 [[[[.,.],.],.],.]=>[1,2,3,4]=>0 [.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>4 [.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>3 [.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>3 [.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>3 [.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>2 [.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>3 [.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>2 [.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>3 [.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>2 [.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>3 [.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>2 [.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>2 [.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>2 [.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>1 [[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>3 [[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>2 [[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>2 [[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>2 [[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>1 [[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>3 [[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>2 [[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>2 [[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>1 [[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>3 [[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>2 [[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>2 [[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>2 [[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>1 [[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>3 [[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>2 [[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>2 [[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>2 [[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>1 [[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>2 [[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>1 [[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>2 [[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>1 [[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>2 [[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>1 [[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>1 [[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>1 [[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0 [.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>5 [.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>4 [.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>4 [.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>4 [.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>3 [.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>4 [.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>3 [.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>4 [.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>3 [.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>4 [.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>3 [.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>3 [.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>3 [.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>2 [.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>4 [.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>3 [.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>3 [.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>3 [.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>2 [.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>4 [.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>3 [.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>3 [.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>2 [.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>4 [.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>3 [.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>3 [.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>3 [.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>2 [.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>4 [.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>3 [.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>3 [.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>3 [.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>2 [.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>3 [.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>2 [.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>3 [.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>2 [.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>3 [.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>2 [.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>2 [.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>2 [.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>1 [[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>4 [[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>3 [[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>3 [[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>3 [[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>2 [[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>3 [[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>2 [[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>3 [[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>2 [[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>3 [[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>2 [[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>2 [[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>2 [[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>1 [[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>4 [[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>3 [[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>3 [[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>3 [[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>2 [[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>3 [[[.,.],.],[.,[[.,.],.]]]=>[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]=>1 [[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>4 [[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>3 [[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>3 [[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>2 [[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>3 [[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>2 [[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>3 [[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>2 [[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>2 [[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>1 [[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>4 [[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>3 [[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>3 [[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>3 [[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>2 [[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>3 [[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>2 [[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>3 [[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>2 [[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>3 [[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>2 [[[[.,.],[.,.]],.],[.,.]]=>[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]=>4 [[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>3 [[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>3 [[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>3 [[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>2 [[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>3 [[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>2 [[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>3 [[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>2 [[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>3 [[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>2 [[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>2 [[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>2 [[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>1 [[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>3 [[[.,.],[.,[[.,.],.]]],.]=>[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]=>1 [[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>3 [[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>2 [[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>2 [[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>1 [[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>3 [[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>2 [[[[.,.],[.,.]],[.,.]],.]=>[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]=>3 [[[.,[.,[[.,.],.]]],.],.]=>[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]=>1 [[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>2 [[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>1 [[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>2 [[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>1 [[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>2 [[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>1 [[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>1 [[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>1 [[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>0
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Description
The number of non-left-to-right-maxima of a permutation.
An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a **non-left-to-right-maximum** if there exists a $j < i$ such that $\sigma_j > \sigma_i$.
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.