Identifier
Values
[1] => [1,0] => [1] => [1] => 0
[2] => [1,0,1,0] => [2,1] => [2,1] => 1
[1,1] => [1,1,0,0] => [1,2] => [1,2] => 0
[3] => [1,0,1,0,1,0] => [2,3,1] => [2,3,1] => 2
[2,1] => [1,0,1,1,0,0] => [2,1,3] => [2,1,3] => 1
[1,1,1] => [1,1,0,1,0,0] => [3,1,2] => [3,1,2] => 2
[4] => [1,0,1,0,1,0,1,0] => [2,3,4,1] => [2,3,4,1] => 3
[3,1] => [1,0,1,0,1,1,0,0] => [2,3,1,4] => [2,3,1,4] => 2
[2,2] => [1,1,1,0,0,0] => [1,2,3] => [1,2,3] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [2,4,1,3] => [2,4,1,3] => 3
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [3,4,1,2] => [3,4,1,2] => 2
[3,2] => [1,0,1,1,1,0,0,0] => [2,1,3,4] => [2,1,3,4] => 1
[2,2,1] => [1,1,1,0,0,1,0,0] => [1,4,2,3] => [1,4,2,3] => 2
[3,3] => [1,1,1,0,1,0,0,0] => [4,1,2,3] => [4,1,2,3] => 3
[2,2,2] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,2,3,4] => 0
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [1,4,5,2,3] => [1,4,5,2,3] => 2
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [1,2,5,3,4] => [1,2,5,3,4] => 2
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [1,2,3,4,5] => 0
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
click to show known generating functions       
Description
The reflection length of a signed permutation.
This is the minimal numbers of reflections needed to express a signed permutation.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to signed permutation
Description
The signed permutation with all signs positive.