Identifier
Values
{{1,2}} => [2,1] => [1,2] => [1,2] => 1
{{1},{2}} => [1,2] => [2,1] => [2,1] => 0
{{1,2,3}} => [2,3,1] => [1,3,2] => [1,3,2] => 2
{{1,2},{3}} => [2,1,3] => [3,1,2] => [3,1,2] => 1
{{1,3},{2}} => [3,2,1] => [1,2,3] => [1,2,3] => 3
{{1},{2,3}} => [1,3,2] => [2,3,1] => [1,3,2] => 2
{{1},{2},{3}} => [1,2,3] => [3,2,1] => [3,2,1] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 3
{{1,2,3},{4}} => [2,3,1,4] => [4,1,3,2] => [4,1,3,2] => 2
{{1,2,4},{3}} => [2,4,3,1] => [1,3,4,2] => [1,2,4,3] => 5
{{1,2},{3,4}} => [2,1,4,3] => [3,4,1,2] => [2,4,1,3] => 3
{{1,2},{3},{4}} => [2,1,3,4] => [4,3,1,2] => [4,3,1,2] => 1
{{1,3,4},{2}} => [3,2,4,1] => [1,4,2,3] => [1,4,2,3] => 4
{{1,3},{2,4}} => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 4
{{1,3},{2},{4}} => [3,2,1,4] => [4,1,2,3] => [4,1,2,3] => 3
{{1,4},{2,3}} => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 6
{{1},{2,3,4}} => [1,3,4,2] => [2,4,3,1] => [1,4,3,2] => 3
{{1},{2,3},{4}} => [1,3,2,4] => [4,2,3,1] => [4,1,3,2] => 2
{{1,4},{2},{3}} => [4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 5
{{1},{2,4},{3}} => [1,4,3,2] => [2,3,4,1] => [1,2,4,3] => 5
{{1},{2},{3,4}} => [1,2,4,3] => [3,4,2,1] => [1,4,3,2] => 3
{{1},{2},{3},{4}} => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
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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
Inverse fireworks map
Description
Sends a permutation to an inverse fireworks permutation.
A permutation $\sigma$ is inverse fireworks if its inverse avoids the vincular pattern $3-12$. The inverse fireworks map sends any permutation $\sigma$ to an inverse fireworks permutation that is below $\sigma$ in left weak order and has the same Rajchgot index St001759The Rajchgot index of a permutation..
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.