Identifier
-
Mp00170:
Permutations
—to signed permutation⟶
Signed permutations
St001772: Signed permutations ⟶ ℤ
Values
[1] => [1] => 0
[1,2] => [1,2] => 1
[2,1] => [2,1] => 0
[1,2,3] => [1,2,3] => 3
[1,3,2] => [1,3,2] => 2
[2,1,3] => [2,1,3] => 2
[2,3,1] => [2,3,1] => 1
[3,1,2] => [3,1,2] => 1
[3,2,1] => [3,2,1] => 0
[1,2,3,4] => [1,2,3,4] => 6
[1,2,4,3] => [1,2,4,3] => 5
[1,3,2,4] => [1,3,2,4] => 5
[1,3,4,2] => [1,3,4,2] => 4
[1,4,2,3] => [1,4,2,3] => 4
[1,4,3,2] => [1,4,3,2] => 3
[2,1,3,4] => [2,1,3,4] => 5
[2,1,4,3] => [2,1,4,3] => 4
[2,3,1,4] => [2,3,1,4] => 4
[2,3,4,1] => [2,3,4,1] => 3
[2,4,1,3] => [2,4,1,3] => 3
[2,4,3,1] => [2,4,3,1] => 2
[3,1,2,4] => [3,1,2,4] => 4
[3,1,4,2] => [3,1,4,2] => 3
[3,2,1,4] => [3,2,1,4] => 3
[3,2,4,1] => [3,2,4,1] => 2
[3,4,1,2] => [3,4,1,2] => 2
[3,4,2,1] => [3,4,2,1] => 1
[4,1,2,3] => [4,1,2,3] => 3
[4,1,3,2] => [4,1,3,2] => 2
[4,2,1,3] => [4,2,1,3] => 2
[4,2,3,1] => [4,2,3,1] => 1
[4,3,1,2] => [4,3,1,2] => 1
[4,3,2,1] => [4,3,2,1] => 0
[1,2,3,4,5] => [1,2,3,4,5] => 10
[1,2,3,5,4] => [1,2,3,5,4] => 9
[1,2,4,3,5] => [1,2,4,3,5] => 9
[1,2,4,5,3] => [1,2,4,5,3] => 8
[1,2,5,3,4] => [1,2,5,3,4] => 8
[1,2,5,4,3] => [1,2,5,4,3] => 7
[1,3,2,4,5] => [1,3,2,4,5] => 9
[1,3,2,5,4] => [1,3,2,5,4] => 8
[1,3,4,2,5] => [1,3,4,2,5] => 8
[1,3,4,5,2] => [1,3,4,5,2] => 7
[1,3,5,2,4] => [1,3,5,2,4] => 7
[1,3,5,4,2] => [1,3,5,4,2] => 6
[1,4,2,3,5] => [1,4,2,3,5] => 8
[1,4,2,5,3] => [1,4,2,5,3] => 7
[1,4,3,2,5] => [1,4,3,2,5] => 7
[1,4,3,5,2] => [1,4,3,5,2] => 6
[1,4,5,2,3] => [1,4,5,2,3] => 6
[1,4,5,3,2] => [1,4,5,3,2] => 5
[1,5,2,3,4] => [1,5,2,3,4] => 7
[1,5,2,4,3] => [1,5,2,4,3] => 6
[1,5,3,2,4] => [1,5,3,2,4] => 6
[1,5,3,4,2] => [1,5,3,4,2] => 5
[1,5,4,2,3] => [1,5,4,2,3] => 5
[1,5,4,3,2] => [1,5,4,3,2] => 4
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Description
The number of occurrences of the signed pattern 12 in a signed permutation.
This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < \pi(j)$.
This is the number of pairs $1\leq i < j\leq n$ such that $0 < \pi(i) < \pi(j)$.
Map
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Description
The signed permutation with all signs positive.
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