Identifier
Values
[1,0,1,0] => [1,2] => 0
[1,1,0,0] => [2,1] => 0
[1,0,1,0,1,0] => [1,2,3] => 0
[1,0,1,1,0,0] => [1,3,2] => 1
[1,1,0,0,1,0] => [2,1,3] => 1
[1,1,0,1,0,0] => [2,3,1] => 1
[1,1,1,0,0,0] => [3,2,1] => 0
[1,0,1,0,1,0,1,0] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [1,3,2,4] => 2
[1,0,1,1,0,1,0,0] => [1,3,4,2] => 2
[1,0,1,1,1,0,0,0] => [1,4,3,2] => 1
[1,1,0,0,1,0,1,0] => [2,1,3,4] => 1
[1,1,0,0,1,1,0,0] => [2,1,4,3] => 1
[1,1,0,1,0,0,1,0] => [2,3,1,4] => 2
[1,1,0,1,0,1,0,0] => [2,3,4,1] => 1
[1,1,0,1,1,0,0,0] => [2,4,3,1] => 2
[1,1,1,0,0,0,1,0] => [3,2,1,4] => 1
[1,1,1,0,0,1,0,0] => [3,2,4,1] => 2
[1,1,1,0,1,0,0,0] => [3,4,2,1] => 1
[1,1,1,1,0,0,0,0] => [4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 0
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 2
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 2
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 2
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 3
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 2
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 3
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 2
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 3
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => 2
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 2
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 2
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 2
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 2
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => 1
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => 2
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 3
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => 3
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => 3
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => 2
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 1
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 3
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => 2
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => 2
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => 2
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => 2
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => 2
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => 2
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => 1
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => 1
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => 4
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => 4
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => 4
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => 3
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => 4
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => 2
>>> Load all 195 entries. <<<
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => 1
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => 3
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => 3
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => 1
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => 0
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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Description
The number of non-attacking neighbors of a permutation.
For a permutation $\sigma$, the indices $i$ and $i+1$ are attacking if $|\sigma(i)-\sigma(i+1)| = 1$.
Visually, this is, for $\sigma$ considered as a placement of kings on a chessboard, if the kings placed in columns $i$ and $i+1$ are non-attacking.
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).