Identifier
Values
[1] => [1] => [1] => [-1] => 1
[1,2] => [1,2] => [1,2] => [-2,1] => 2
[2,1] => [2,1] => [2,1] => [1,-2] => 1
[1,2,3] => [1,2,3] => [1,2,3] => [-3,1,2] => 3
[1,3,2] => [1,3,2] => [1,3,2] => [-3,2,1] => 3
[2,1,3] => [2,1,3] => [2,1,3] => [1,-3,2] => 2
[2,3,1] => [3,1,2] => [3,1,2] => [2,-3,1] => 3
[3,1,2] => [2,3,1] => [2,3,1] => [2,1,-3] => 2
[3,2,1] => [3,2,1] => [3,2,1] => [1,2,-3] => 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [-4,1,2,3] => 4
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [-4,1,3,2] => 4
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [-4,2,1,3] => 4
[1,3,4,2] => [1,4,2,3] => [1,4,2,3] => [-4,3,1,2] => 4
[1,4,2,3] => [1,3,4,2] => [1,3,4,2] => [-4,2,3,1] => 5
[1,4,3,2] => [1,4,3,2] => [1,4,3,2] => [-4,3,2,1] => 4
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [1,-4,2,3] => 3
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [1,-4,3,2] => 3
[2,3,1,4] => [3,1,2,4] => [3,1,2,4] => [2,-4,1,3] => 4
[2,3,4,1] => [4,1,2,3] => [4,1,2,3] => [3,-4,1,2] => 5
[2,4,1,3] => [3,1,4,2] => [3,1,4,2] => [2,-4,3,1] => 4
[2,4,3,1] => [4,1,3,2] => [4,1,3,2] => [3,-4,2,1] => 4
[3,1,2,4] => [2,3,1,4] => [2,3,1,4] => [2,1,-4,3] => 3
[3,1,4,2] => [2,4,1,3] => [2,4,1,3] => [3,1,-4,2] => 4
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [1,2,-4,3] => 2
[3,2,4,1] => [4,2,1,3] => [4,2,1,3] => [1,3,-4,2] => 3
[3,4,1,2] => [3,4,1,2] => [3,4,1,2] => [3,2,-4,1] => 4
[3,4,2,1] => [4,3,1,2] => [4,3,1,2] => [2,3,-4,1] => 4
[4,1,2,3] => [2,3,4,1] => [2,3,4,1] => [3,1,2,-4] => 3
[4,1,3,2] => [2,4,3,1] => [2,4,3,1] => [3,2,1,-4] => 3
[4,2,1,3] => [3,2,4,1] => [3,2,4,1] => [1,3,2,-4] => 2
[4,2,3,1] => [4,2,3,1] => [4,2,3,1] => [2,3,1,-4] => 3
[4,3,1,2] => [3,4,2,1] => [3,4,2,1] => [2,1,3,-4] => 2
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [1,2,3,-4] => 1
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [1,-5,2,3,4] => 4
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [1,-5,2,4,3] => 4
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [1,-5,3,2,4] => 4
[2,1,4,5,3] => [2,1,5,3,4] => [2,1,5,3,4] => [1,-5,4,2,3] => 4
[2,1,5,3,4] => [2,1,4,5,3] => [2,1,4,5,3] => [1,-5,3,4,2] => 5
[2,1,5,4,3] => [2,1,5,4,3] => [2,1,5,4,3] => [1,-5,4,3,2] => 4
[3,2,1,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => [1,2,-5,3,4] => 3
[3,2,1,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => [1,2,-5,4,3] => 3
[3,2,4,1,5] => [4,2,1,3,5] => [4,2,1,3,5] => [1,3,-5,2,4] => 4
[3,2,4,5,1] => [5,2,1,3,4] => [5,2,1,3,4] => [1,4,-5,2,3] => 5
[3,2,5,1,4] => [4,2,1,5,3] => [4,2,1,5,3] => [1,3,-5,4,2] => 4
[3,2,5,4,1] => [5,2,1,4,3] => [5,2,1,4,3] => [1,4,-5,3,2] => 4
[4,2,1,3,5] => [3,2,4,1,5] => [3,2,4,1,5] => [1,3,2,-5,4] => 3
[4,2,1,5,3] => [3,2,5,1,4] => [3,2,5,1,4] => [1,4,2,-5,3] => 4
[4,2,5,1,3] => [4,2,5,1,3] => [4,2,5,1,3] => [1,4,3,-5,2] => 4
[4,3,2,1,5] => [4,3,2,1,5] => [4,3,2,1,5] => [1,2,3,-5,4] => 2
[4,3,2,5,1] => [5,3,2,1,4] => [5,3,2,1,4] => [1,2,4,-5,3] => 3
[4,3,5,2,1] => [5,4,2,1,3] => [5,4,2,1,3] => [1,3,4,-5,2] => 4
[5,2,1,3,4] => [3,2,4,5,1] => [3,2,4,5,1] => [1,4,2,3,-5] => 3
[5,2,1,4,3] => [3,2,5,4,1] => [3,2,5,4,1] => [1,4,3,2,-5] => 3
[5,3,2,1,4] => [4,3,2,5,1] => [4,3,2,5,1] => [1,2,4,3,-5] => 2
[5,3,2,4,1] => [5,3,2,4,1] => [5,3,2,4,1] => [1,3,4,2,-5] => 3
[5,4,2,1,3] => [4,3,5,2,1] => [4,3,5,2,1] => [1,3,2,4,-5] => 2
[5,4,3,2,1] => [5,4,3,2,1] => [5,4,3,2,1] => [1,2,3,4,-5] => 1
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Description
The number of Bruhat lower covers of a permutation.
This is, for a signed permutation $\pi$, the number of signed permutations $\tau$ having a reduced word which is obtained by deleting a letter from a reduced word from $\pi$.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
inverse
Description
Sends a permutation to its inverse.
Map
rowmotion
Description
The rowmotion of a signed permutation with respect to the sorting order.
The sorting order on signed permutations (with respect to the Coxeter element $-n, 1, 2,\dots, n-1$) is defined in [1].