Identifier
Values
[1,1] => [1] => [1,0] => 10 => 1
[2,1] => [1] => [1,0] => 10 => 1
[1,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[3,1] => [1] => [1,0] => 10 => 1
[2,2] => [2] => [1,0,1,0] => 1010 => 0
[2,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[4,1] => [1] => [1,0] => 10 => 1
[3,2] => [2] => [1,0,1,0] => 1010 => 0
[3,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[5,1] => [1] => [1,0] => 10 => 1
[4,2] => [2] => [1,0,1,0] => 1010 => 0
[4,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[6,1] => [1] => [1,0] => 10 => 1
[5,2] => [2] => [1,0,1,0] => 1010 => 0
[5,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[7,1] => [1] => [1,0] => 10 => 1
[6,2] => [2] => [1,0,1,0] => 1010 => 0
[6,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[8,1] => [1] => [1,0] => 10 => 1
[7,2] => [2] => [1,0,1,0] => 1010 => 0
[7,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[9,1] => [1] => [1,0] => 10 => 1
[8,2] => [2] => [1,0,1,0] => 1010 => 0
[8,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[10,1] => [1] => [1,0] => 10 => 1
[9,2] => [2] => [1,0,1,0] => 1010 => 0
[9,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[11,1] => [1] => [1,0] => 10 => 1
[10,2] => [2] => [1,0,1,0] => 1010 => 0
[10,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[12,1] => [1] => [1,0] => 10 => 1
[11,2] => [2] => [1,0,1,0] => 1010 => 0
[11,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[13,1] => [1] => [1,0] => 10 => 1
[12,2] => [2] => [1,0,1,0] => 1010 => 0
[12,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[14,1] => [1] => [1,0] => 10 => 1
[13,2] => [2] => [1,0,1,0] => 1010 => 0
[13,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[15,1] => [1] => [1,0] => 10 => 1
[14,2] => [2] => [1,0,1,0] => 1010 => 0
[14,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
[16,1] => [1] => [1,0] => 10 => 1
[15,2] => [2] => [1,0,1,0] => 1010 => 0
[15,1,1] => [1,1] => [1,1,0,0] => 1100 => 1
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Map
first row removal
Description
Removes the first entry of an integer 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
to binary word
Description
Return the Dyck word as binary word.