Identifier
Values
[1] => [1] => [1,0,1,0] => 1
[2] => [1,1] => [1,0,1,1,0,0] => 2
[1,1] => [2] => [1,1,0,0,1,0] => 1
[1,1,1] => [3] => [1,1,1,0,0,0,1,0] => 1
[3,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
[1,1,1,1] => [4] => [1,1,1,1,0,0,0,0,1,0] => 1
[2,2,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 3
[1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[4,1,1] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 2
[3,3] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
[2,2,2] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 5
[2,2,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
[1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[2,2,2,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 4
[2,2,1,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 7
[5,3] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[5,1,1,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[4,2,2] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,3,1,1] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 3
[2,2,2,2] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 6
[2,2,2,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 7
[2,2,1,1,1,1] => [6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 9
[6,3] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[4,4,1] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[3,3,1,1,1] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 5
[2,2,2,2,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 5
[2,2,2,1,1,1] => [6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 10
[7,3] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[6,1,1,1,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 2
[5,2,2,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 6
[3,3,3,1] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
[3,3,1,1,1,1] => [6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[2,2,2,2,2] => [5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 7
[2,2,2,2,1,1] => [6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[6,4,1] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[5,2,2,2] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
[4,4,1,1,1] => [5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
[3,3,3,1,1] => [5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 4
[2,2,2,2,2,1] => [6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 6
[7,4,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[6,2,2,1,1] => [5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 8
[5,5,1,1] => [4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[5,3,3,1] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 4
[4,4,4] => [3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[4,4,1,1,1,1] => [6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 5
[3,3,3,3] => [4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 7
[3,3,3,1,1,1] => [6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[6,2,2,2,1] => [5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[4,4,2,2,1] => [5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 5
[3,3,3,3,1] => [5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[7,5,1,1] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[6,4,4] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[6,3,3,1,1] => [5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 6
[6,2,2,2,2] => [5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 6
[5,5,2,2] => [4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 7
[5,5,1,1,1,1] => [6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 3
[5,3,3,3] => [4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 7
[4,4,4,1,1] => [5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[3,3,3,3,1,1] => [6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 5
[7,4,4] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[4,4,4,1,1,1] => [6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 4
[4,4,2,2,2,1] => [6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 8
[7,5,2,2] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[6,6,4] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[6,4,4,1,1] => [5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 4
[6,3,3,3,1] => [5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[5,5,3,3] => [4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[5,5,2,2,1,1] => [6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 7
[4,4,4,2,2] => [5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 7
[5,5,2,2,2,1] => [6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 6
[4,4,4,2,2,1] => [6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 6
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 indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
Bulgarian solitaire
Description
A move in Bulgarian solitaire.
Remove the first column of the Ferrers diagram and insert it as a new row.
If the partition is empty, return the empty partition.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.