Identifier
Values
[1,2] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [1,2] => 1
[1,2,3] => [3,2,1] => [3,2,1] => 0
[1,3,2] => [2,3,1] => [3,1,2] => 1
[2,1,3] => [3,1,2] => [1,3,2] => 2
[2,3,1] => [1,3,2] => [2,3,1] => 1
[3,1,2] => [2,1,3] => [2,1,3] => 2
[3,2,1] => [1,2,3] => [1,2,3] => 3
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[1,2,4,3] => [3,4,2,1] => [4,3,1,2] => 1
[1,3,2,4] => [4,2,3,1] => [4,1,3,2] => 2
[1,3,4,2] => [2,4,3,1] => [4,2,3,1] => 1
[1,4,2,3] => [3,2,4,1] => [4,2,1,3] => 2
[1,4,3,2] => [2,3,4,1] => [4,1,2,3] => 3
[2,1,3,4] => [4,3,1,2] => [1,4,3,2] => 3
[2,1,4,3] => [3,4,1,2] => [1,4,2,3] => 4
[2,3,1,4] => [4,1,3,2] => [2,4,3,1] => 2
[2,3,4,1] => [1,4,3,2] => [3,4,2,1] => 1
[2,4,1,3] => [3,1,4,2] => [3,4,1,2] => 2
[2,4,3,1] => [1,3,4,2] => [2,4,1,3] => 3
[3,1,2,4] => [4,2,1,3] => [3,1,4,2] => 3
[3,1,4,2] => [2,4,1,3] => [1,3,4,2] => 4
[3,2,1,4] => [4,1,2,3] => [1,2,4,3] => 5
[3,2,4,1] => [1,4,2,3] => [2,1,4,3] => 4
[3,4,1,2] => [2,1,4,3] => [3,2,4,1] => 2
[3,4,2,1] => [1,2,4,3] => [2,3,4,1] => 3
[4,1,2,3] => [3,2,1,4] => [3,2,1,4] => 3
[4,1,3,2] => [2,3,1,4] => [3,1,2,4] => 4
[4,2,1,3] => [3,1,2,4] => [1,3,2,4] => 5
[4,2,3,1] => [1,3,2,4] => [2,3,1,4] => 4
[4,3,1,2] => [2,1,3,4] => [2,1,3,4] => 5
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 6
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Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.