Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
St000433: Permutations ⟶ ℤ
Values
{{1}} => [1] => 0
{{1,2}} => [2,1] => 0
{{1},{2}} => [1,2] => 0
{{1,2,3}} => [2,3,1] => 0
{{1,2},{3}} => [2,1,3] => 0
{{1,3},{2}} => [3,2,1] => 1
{{1},{2,3}} => [1,3,2] => 1
{{1},{2},{3}} => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => 0
{{1,2,3},{4}} => [2,3,1,4] => 0
{{1,2,4},{3}} => [2,4,3,1] => 2
{{1,2},{3,4}} => [2,1,4,3] => 2
{{1,2},{3},{4}} => [2,1,3,4] => 0
{{1,3,4},{2}} => [3,2,4,1] => 1
{{1,3},{2,4}} => [3,4,1,2] => 0
{{1,3},{2},{4}} => [3,2,1,4] => 1
{{1,4},{2,3}} => [4,3,2,1] => 4
{{1},{2,3,4}} => [1,3,4,2] => 2
{{1},{2,3},{4}} => [1,3,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => 2
{{1},{2,4},{3}} => [1,4,3,2] => 4
{{1},{2},{3,4}} => [1,2,4,3] => 2
{{1},{2},{3},{4}} => [1,2,3,4] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => 0
{{1,2,3,5},{4}} => [2,3,5,4,1] => 3
{{1,2,3},{4,5}} => [2,3,1,5,4] => 3
{{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
{{1,2,4,5},{3}} => [2,4,3,5,1] => 2
{{1,2,4},{3,5}} => [2,4,5,1,3] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => 2
{{1,2,5},{3,4}} => [2,5,4,3,1] => 7
{{1,2},{3,4,5}} => [2,1,4,5,3] => 4
{{1,2},{3,4},{5}} => [2,1,4,3,5] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => 4
{{1,2},{3,5},{4}} => [2,1,5,4,3] => 7
{{1,2},{3},{4,5}} => [2,1,3,5,4] => 3
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => 0
{{1,3,4,5},{2}} => [3,2,4,5,1] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => 3
{{1,3,4},{2},{5}} => [3,2,4,1,5] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => 3
{{1,3},{2,4,5}} => [3,4,1,5,2] => 1
{{1,3},{2,4},{5}} => [3,4,1,2,5] => 0
{{1,3,5},{2},{4}} => [3,2,5,4,1] => 4
{{1,3},{2,5},{4}} => [3,5,1,4,2] => 3
{{1,3},{2},{4,5}} => [3,2,1,5,4] => 4
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => 4
{{1,4},{2,3,5}} => [4,3,5,1,2] => 2
{{1,4},{2,3},{5}} => [4,3,2,1,5] => 4
{{1,5},{2,3,4}} => [5,3,4,2,1] => 7
{{1},{2,3,4,5}} => [1,3,4,5,2] => 3
{{1},{2,3,4},{5}} => [1,3,4,2,5] => 2
{{1,5},{2,3},{4}} => [5,3,2,4,1] => 5
{{1},{2,3,5},{4}} => [1,3,5,4,2] => 6
{{1},{2,3},{4,5}} => [1,3,2,5,4] => 4
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => 2
{{1,4},{2,5},{3}} => [4,5,3,1,2] => 4
{{1,4},{2},{3,5}} => [4,2,5,1,3] => 2
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => 10
{{1},{2,4,5},{3}} => [1,4,3,5,2] => 5
{{1},{2,4},{3,5}} => [1,4,5,2,3] => 4
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => 4
{{1,5},{2},{3,4}} => [5,2,4,3,1] => 6
{{1},{2,5},{3,4}} => [1,5,4,3,2] => 10
{{1},{2},{3,4,5}} => [1,2,4,5,3] => 4
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => 2
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => 3
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => 7
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => 7
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => 3
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => 0
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => 4
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 4
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => 0
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => 3
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 4
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 3
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => 10
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 6
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 3
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 6
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 10
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 4
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => 0
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => 2
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => 7
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 2
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 6
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 4
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 2
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 6
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 7
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 6
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 7
>>> Load all 741 entries. <<<
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of occurrences of the pattern 132 or of the pattern 321 in a permutation.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!