Identifier
Values
[1] => [1] => 0
[1,2] => [1,2] => 0
[2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => 2
[2,3,1] => [2,3,1] => 2
[3,1,2] => [3,1,2] => 2
[3,2,1] => [3,2,1] => 4
[1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => 2
[1,3,2,4] => [1,3,2,4] => 2
[1,3,4,2] => [1,3,4,2] => 2
[1,4,2,3] => [1,4,2,3] => 2
[1,4,3,2] => [1,4,3,2] => 4
[2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [2,3,1,4] => 2
[2,3,4,1] => [2,3,4,1] => 2
[2,4,1,3] => [2,4,1,3] => 2
[2,4,3,1] => [2,4,3,1] => 4
[3,1,2,4] => [3,1,2,4] => 2
[3,1,4,2] => [3,1,4,2] => 4
[3,2,1,4] => [3,2,1,4] => 4
[3,2,4,1] => [3,2,4,1] => 4
[3,4,1,2] => [3,4,1,2] => 2
[3,4,2,1] => [3,4,2,1] => 4
[4,1,2,3] => [4,1,2,3] => 2
[4,1,3,2] => [4,1,3,2] => 4
[4,2,1,3] => [4,2,1,3] => 4
[4,2,3,1] => [4,2,3,1] => 4
[4,3,1,2] => [4,3,1,2] => 4
[4,3,2,1] => [4,3,2,1] => 6
[1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => [1,2,4,5,3] => 2
[1,2,5,3,4] => [1,2,5,3,4] => 2
[1,2,5,4,3] => [1,2,5,4,3] => 4
[1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => [1,3,2,5,4] => 4
[1,3,4,2,5] => [1,3,4,2,5] => 2
[1,3,4,5,2] => [1,3,4,5,2] => 2
[1,3,5,2,4] => [1,3,5,2,4] => 2
[1,3,5,4,2] => [1,3,5,4,2] => 4
[1,4,2,3,5] => [1,4,2,3,5] => 2
[1,4,2,5,3] => [1,4,2,5,3] => 4
[1,4,3,2,5] => [1,4,3,2,5] => 4
[1,4,3,5,2] => [1,4,3,5,2] => 4
[1,4,5,2,3] => [1,4,5,2,3] => 2
[1,4,5,3,2] => [1,4,5,3,2] => 4
[1,5,2,3,4] => [1,5,2,3,4] => 2
[1,5,2,4,3] => [1,5,2,4,3] => 4
[1,5,3,2,4] => [1,5,3,2,4] => 4
[1,5,3,4,2] => [1,5,3,4,2] => 4
[1,5,4,2,3] => [1,5,4,2,3] => 4
[1,5,4,3,2] => [1,5,4,3,2] => 6
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Description
The flag descent of a signed permutation.
$$ fdes(\sigma) = 2 \lvert \{ i \in [n-1] \mid \sigma(i) > \sigma(i+1) \} \rvert + \chi( \sigma(1) < 0 ) $$
It has the same distribution as the flag excedance statistic.
Map
to signed permutation
Description
The signed permutation with all signs positive.