Identifier
Values
[[1,1],[]] => [1,1] => [2] => [1,0,1,0] => 2
[[2,1],[1]] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 2
[[3],[]] => [3] => [3] => [1,0,1,0,1,0] => 3
[[2,1],[]] => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 2
[[3,1],[1]] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[[2,2],[1]] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 3
[[3,2],[2]] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[1,1,1],[]] => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 2
[[2,2,1],[1,1]] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[2,1,1],[1]] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[[4],[]] => [4] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 3
[[3,1],[]] => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 3
[[4,1],[1]] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[[2,2],[]] => [2,2] => [4] => [1,0,1,0,1,0,1,0] => 3
[[3,2],[1]] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[2,1,1],[]] => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
[[3,1,1],[1]] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[[2,2,1],[1]] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[3,2,2],[2,1]] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[2,2,1,1],[1,1]] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[2,1,1,1],[1]] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[[5],[]] => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 3
[[4,1],[]] => [4,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 4
[[3,2],[]] => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 3
[[3,1,1],[]] => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 2
[[2,2,1],[]] => [2,2,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 3
[[3,2,2],[1,1]] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[2,1,1,1],[]] => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
[[3,1,1,1],[1]] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[3,2,2],[2]] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[2,2,1,1],[1]] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[2,2,2,2],[1,1,1]] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,1,1,1,1],[]] => [1,1,1,1,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 2
[[2,1,1,1,1],[1]] => [2,1,1,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[6],[]] => [6] => [3,3] => [1,1,1,0,1,0,0,0] => 2
[[6,1],[1]] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[3,1,1,1],[]] => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 3
[[3,2,2],[1]] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[2,2,1,1],[]] => [2,2,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 3
[[2,1,1,1,1],[]] => [2,1,1,1,1] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 3
[[3,1,1,1,1],[1]] => [3,1,1,1,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2,2],[1,1]] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[6,1],[]] => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 3
[[6,1,1],[1]] => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[[3,2,2],[]] => [3,2,2] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 3
[[3,1,1,1,1],[]] => [3,1,1,1,1] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 2
[[2,2,2,2],[1]] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 2
[[6,1,1],[]] => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
[[2,2,2,2],[]] => [2,2,2,2] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 3
[[1,1,1,1,1,1,1,1],[]] => [1,1,1,1,1,1,1,1] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 2
search for individual values
searching the database for the individual values of this statistic
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Map
outer shape
Description
The outer shape of the skew partition.
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
Glaisher-Franklin inverse
Description
The Glaisher-Franklin bijection on integer partitions.
This map sends the number of distinct repeated part sizes to the number of distinct even part sizes, see [1, 3.3.1].