Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
St000570: Permutations ⟶ ℤ
Values
{{1,2}} => [2,1] => 1
{{1},{2}} => [1,2] => 1
{{1,2,3}} => [2,3,1] => 1
{{1,2},{3}} => [2,1,3] => 1
{{1,3},{2}} => [3,2,1] => 1
{{1},{2,3}} => [1,3,2] => 1
{{1},{2},{3}} => [1,2,3] => 1
{{1,2,3,4}} => [2,3,4,1] => 1
{{1,2,3},{4}} => [2,3,1,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => 1
{{1,2},{3,4}} => [2,1,4,3] => 2
{{1,2},{3},{4}} => [2,1,3,4] => 1
{{1,3,4},{2}} => [3,2,4,1] => 1
{{1,3},{2,4}} => [3,4,1,2] => 1
{{1,3},{2},{4}} => [3,2,1,4] => 1
{{1,4},{2,3}} => [4,3,2,1] => 1
{{1},{2,3,4}} => [1,3,4,2] => 1
{{1},{2,3},{4}} => [1,3,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => 1
{{1},{2,4},{3}} => [1,4,3,2] => 1
{{1},{2},{3,4}} => [1,2,4,3] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => 1
{{1,2,3,4,5}} => [2,3,4,5,1] => 1
{{1,2,3,4},{5}} => [2,3,4,1,5] => 1
{{1,2,3,5},{4}} => [2,3,5,4,1] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => 2
{{1,2,3},{4},{5}} => [2,3,1,4,5] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => 1
{{1,2,4},{3},{5}} => [2,4,3,1,5] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => 1
{{1,2},{3,4,5}} => [2,1,4,5,3] => 2
{{1,2},{3,4},{5}} => [2,1,4,3,5] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => 1
{{1,2},{3,5},{4}} => [2,1,5,4,3] => 3
{{1,2},{3},{4,5}} => [2,1,3,5,4] => 2
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => 1
{{1,3,4},{2},{5}} => [3,2,4,1,5] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => 1
{{1,3},{2,4,5}} => [3,4,1,5,2] => 1
{{1,3},{2,4},{5}} => [3,4,1,2,5] => 1
{{1,3,5},{2},{4}} => [3,2,5,4,1] => 2
{{1,3},{2,5},{4}} => [3,5,1,4,2] => 1
{{1,3},{2},{4,5}} => [3,2,1,5,4] => 3
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => 1
{{1,4},{2,3,5}} => [4,3,5,1,2] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => 1
{{1,5},{2,3,4}} => [5,3,4,2,1] => 1
{{1},{2,3,4,5}} => [1,3,4,5,2] => 1
{{1},{2,3,4},{5}} => [1,3,4,2,5] => 1
{{1,5},{2,3},{4}} => [5,3,2,4,1] => 1
{{1},{2,3,5},{4}} => [1,3,5,4,2] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => 2
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => 1
{{1,4},{2,5},{3}} => [4,5,3,1,2] => 1
{{1,4},{2},{3,5}} => [4,2,5,1,3] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => 1
{{1,5},{2,4},{3}} => [5,4,3,2,1] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => 1
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => 1
{{1,5},{2},{3,4}} => [5,2,4,3,1] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => 1
{{1},{2},{3,4,5}} => [1,2,4,5,3] => 1
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => 1
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 1
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 1
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 1
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 1
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 2
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 1
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 1
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 1
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 1
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => 1
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 3
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 2
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 1
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 4
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 2
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 1
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 1
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => 1
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 1
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 1
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 2
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 1
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 2
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 2
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 3
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 1
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 1
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => 1
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Description
The Edelman-Greene number of a permutation.
This is the sum of the coefficients of the expansion of the Stanley symmetric function Fω in Schur functions. Equivalently, this is the number of semistandard tableaux whose column words - obtained by reading up columns starting with the leftmost - are reduced words for ω.
This is the sum of the coefficients of the expansion of the Stanley symmetric function Fω in Schur functions. Equivalently, this is the number of semistandard tableaux whose column words - obtained by reading up columns starting with the leftmost - are reduced words for ω.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
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