Identifier
Values
[1] => [1,0] => [1,1,0,0] => [1,2] => 0
[2] => [1,0,1,0] => [1,1,0,1,0,0] => [3,1,2] => 0
[1,1] => [1,1,0,0] => [1,1,1,0,0,0] => [1,2,3] => 0
[3] => [1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [3,4,1,2] => 0
[2,1] => [1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [3,1,2,4] => 0
[1,1,1] => [1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [4,1,2,3] => 0
[4] => [1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [3,4,5,1,2] => 0
[3,1] => [1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [3,4,1,2,5] => 0
[2,2] => [1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [1,2,3,4] => 0
[2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [3,5,1,2,4] => 1
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [4,5,1,2,3] => 0
[3,2] => [1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [3,1,2,4,5] => 0
[2,2,1] => [1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [1,5,2,3,4] => 1
[3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [5,1,2,3,4] => 0
[2,2,2] => [1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [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
Description
The Castelnuovo-Mumford regularity of a permutation.
The Castelnuovo-Mumford regularity of a permutation $\sigma$ is the Castelnuovo-Mumford regularity of the matrix Schubert variety $X_\sigma$.
Equivalently, it is the difference between the degrees of the Grothendieck polynomial and the Schubert polynomial for $\sigma$. It can be computed by subtracting the Coxeter length St000018The number of inversions of a permutation. from the Rajchgot index St001759The Rajchgot index of a permutation..
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
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.