Identifier
-
Mp00080:
Set partitions
—to permutation⟶
Permutations
St000623: Permutations ⟶ ℤ
Values
{{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] => 0
{{1},{2,3}} => [1,3,2] => 0
{{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] => 0
{{1,2},{3,4}} => [2,1,4,3] => 0
{{1,2},{3},{4}} => [2,1,3,4] => 0
{{1,3,4},{2}} => [3,2,4,1] => 0
{{1,3},{2,4}} => [3,4,1,2] => 0
{{1,3},{2},{4}} => [3,2,1,4] => 0
{{1,4},{2,3}} => [4,3,2,1] => 0
{{1},{2,3,4}} => [1,3,4,2] => 0
{{1},{2,3},{4}} => [1,3,2,4] => 0
{{1,4},{2},{3}} => [4,2,3,1] => 0
{{1},{2,4},{3}} => [1,4,3,2] => 0
{{1},{2},{3,4}} => [1,2,4,3] => 0
{{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] => 0
{{1,2,3},{4,5}} => [2,3,1,5,4] => 0
{{1,2,3},{4},{5}} => [2,3,1,4,5] => 0
{{1,2,4,5},{3}} => [2,4,3,5,1] => 0
{{1,2,4},{3,5}} => [2,4,5,1,3] => 0
{{1,2,4},{3},{5}} => [2,4,3,1,5] => 0
{{1,2,5},{3,4}} => [2,5,4,3,1] => 0
{{1,2},{3,4,5}} => [2,1,4,5,3] => 0
{{1,2},{3,4},{5}} => [2,1,4,3,5] => 0
{{1,2,5},{3},{4}} => [2,5,3,4,1] => 0
{{1,2},{3,5},{4}} => [2,1,5,4,3] => 0
{{1,2},{3},{4,5}} => [2,1,3,5,4] => 0
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => 0
{{1,3,4,5},{2}} => [3,2,4,5,1] => 0
{{1,3,4},{2,5}} => [3,5,4,1,2] => 0
{{1,3,4},{2},{5}} => [3,2,4,1,5] => 0
{{1,3,5},{2,4}} => [3,4,5,2,1] => 0
{{1,3},{2,4,5}} => [3,4,1,5,2] => 0
{{1,3},{2,4},{5}} => [3,4,1,2,5] => 0
{{1,3,5},{2},{4}} => [3,2,5,4,1] => 0
{{1,3},{2,5},{4}} => [3,5,1,4,2] => 0
{{1,3},{2},{4,5}} => [3,2,1,5,4] => 0
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => 0
{{1,4,5},{2,3}} => [4,3,2,5,1] => 0
{{1,4},{2,3,5}} => [4,3,5,1,2] => 0
{{1,4},{2,3},{5}} => [4,3,2,1,5] => 0
{{1,5},{2,3,4}} => [5,3,4,2,1] => 0
{{1},{2,3,4,5}} => [1,3,4,5,2] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => 0
{{1,5},{2,3},{4}} => [5,3,2,4,1] => 0
{{1},{2,3,5},{4}} => [1,3,5,4,2] => 0
{{1},{2,3},{4,5}} => [1,3,2,5,4] => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => 0
{{1,4,5},{2},{3}} => [4,2,3,5,1] => 0
{{1,4},{2,5},{3}} => [4,5,3,1,2] => 0
{{1,4},{2},{3,5}} => [4,2,5,1,3] => 0
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => 0
{{1,5},{2,4},{3}} => [5,4,3,2,1] => 0
{{1},{2,4,5},{3}} => [1,4,3,5,2] => 0
{{1},{2,4},{3,5}} => [1,4,5,2,3] => 0
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => 0
{{1,5},{2},{3,4}} => [5,2,4,3,1] => 0
{{1},{2,5},{3,4}} => [1,5,4,3,2] => 0
{{1},{2},{3,4,5}} => [1,2,4,5,3] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => 0
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => 1
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => 0
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => 0
{{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] => 0
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => 0
{{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] => 0
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => 0
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => 0
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => 0
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => 0
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => 0
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => 0
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => 0
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => 0
{{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] => 0
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => 0
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => 0
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => 0
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => 0
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => 0
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => 0
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => 0
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => 0
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => 0
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => 0
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => 0
>>> Load all 411 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 52341 in a permutation.
It is a necessary condition that a permutation π avoids this pattern for the Schubert variety associated to π to have a complete parabolic bundle structure [1].
It is a necessary condition that a permutation π avoids this pattern for the Schubert variety associated to π to have a complete parabolic bundle structure [1].
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!