Identifier
Values
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>1 [1,0,1,0]=>[2,1]=>1 [1,1,0,0]=>[1,2]=>2 [1,0,1,0,1,0]=>[2,3,1]=>2 [1,0,1,1,0,0]=>[2,1,3]=>2 [1,1,0,0,1,0]=>[1,3,2]=>2 [1,1,0,1,0,0]=>[3,1,2]=>1 [1,1,1,0,0,0]=>[1,2,3]=>3 [1,0,1,0,1,0,1,0]=>[2,3,4,1]=>3 [1,0,1,0,1,1,0,0]=>[2,3,1,4]=>3 [1,0,1,1,0,0,1,0]=>[2,1,4,3]=>2 [1,0,1,1,0,1,0,0]=>[2,4,1,3]=>2 [1,0,1,1,1,0,0,0]=>[2,1,3,4]=>3 [1,1,0,0,1,0,1,0]=>[1,3,4,2]=>3 [1,1,0,0,1,1,0,0]=>[1,3,2,4]=>3 [1,1,0,1,0,0,1,0]=>[3,1,4,2]=>2 [1,1,0,1,0,1,0,0]=>[3,4,1,2]=>2 [1,1,0,1,1,0,0,0]=>[3,1,2,4]=>2 [1,1,1,0,0,0,1,0]=>[1,2,4,3]=>3 [1,1,1,0,0,1,0,0]=>[1,4,2,3]=>2 [1,1,1,0,1,0,0,0]=>[4,1,2,3]=>1 [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>4 [1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>4 [1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>4 [1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>3 [1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>3 [1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>4 [1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>3 [1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>3 [1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>3 [1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>3 [1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>3 [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>3 [1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>2 [1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>2 [1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>4 [1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>4 [1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>4 [1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>3 [1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>3 [1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>4 [1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>3 [1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>3 [1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>3 [1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>3 [1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>3 [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>2 [1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>2 [1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>2 [1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>3 [1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>4 [1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>4 [1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>3 [1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>3 [1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>3 [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>2 [1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>2 [1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>2 [1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>2 [1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>4 [1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>3 [1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>2 [1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>1 [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>5 [1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>5 [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>5 [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>4 [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>4 [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>5 [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>4 [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>4 [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>4 [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>4 [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>4 [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>4 [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>3 [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>3 [1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>5 [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>4 [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>4 [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>3 [1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>3 [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>4 [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>4 [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>4 [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>4 [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>4 [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>4 [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>3 [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>3 [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>3 [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>4 [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>4 [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>4 [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>3 [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>3 [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>3 [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>3 [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>3 [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>3 [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>3 [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>4 [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>3 [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>2 [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>2 [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>5 [1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>5 [1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>5 [1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>4 [1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>4 [1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>5 [1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>4 [1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>4 [1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>4 [1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>4 [1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>4 [1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>4 [1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>3 [1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>3 [1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>5 [1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>4 [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>4 [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>3 [1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>3 [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>4 [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>4 [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>4 [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>4 [1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>4 [1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>4 [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>3 [1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>3 [1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>3 [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>4 [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>3 [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>3 [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>3 [1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>3 [1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>3 [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>3 [1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>3 [1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>3 [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>3 [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>3 [1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>2 [1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>2 [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>2 [1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>4 [1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>5 [1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>5 [1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>4 [1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>4 [1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>5 [1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>4 [1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>4 [1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>4 [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>4 [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>4 [1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>3 [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>3 [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>3 [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>4 [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>3 [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>3 [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>3 [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>3 [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>3 [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>3 [1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>3 [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>3 [1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>3 [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>2 [1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>2 [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>2 [1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>2 [1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>3 [1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>5 [1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>5 [1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>4 [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>4 [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>4 [1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>3 [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>3 [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>3 [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>3 [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>2 [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>2 [1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>2 [1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>2 [1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>2 [1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>5 [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>4 [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>3 [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>2 [1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>1 [1,1,1,1,1,1,0,0,0,0,0,0]=>[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 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.