Identifier
Values
([],1) => [1] => 10 => 1
([],2) => [2] => 100 => 1
([(0,1)],2) => [1] => 10 => 1
([(1,2)],3) => [3] => 1000 => 1
([(0,1),(0,2)],3) => [2] => 100 => 1
([(0,2),(2,1)],3) => [1] => 10 => 1
([(0,2),(1,2)],3) => [2] => 100 => 1
([(0,2),(0,3),(3,1)],4) => [3] => 1000 => 1
([(0,1),(0,2),(1,3),(2,3)],4) => [2] => 100 => 1
([(0,3),(3,1),(3,2)],4) => [2] => 100 => 1
([(0,3),(1,3),(3,2)],4) => [2] => 100 => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2] => 1100 => 1
([(0,3),(2,1),(3,2)],4) => [1] => 10 => 1
([(0,3),(1,2),(2,3)],4) => [3] => 1000 => 1
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => [2] => 100 => 1
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => [2,2] => 1100 => 1
([(0,4),(1,4),(4,2),(4,3)],5) => [2,2] => 1100 => 1
([(0,4),(1,4),(2,3),(4,2)],5) => [2] => 100 => 1
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => [2,2] => 1100 => 1
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => [3] => 1000 => 1
([(0,3),(3,4),(4,1),(4,2)],5) => [2] => 100 => 1
([(0,4),(1,2),(2,4),(4,3)],5) => [3] => 1000 => 1
([(0,4),(3,2),(4,1),(4,3)],5) => [3] => 1000 => 1
([(0,4),(2,3),(3,1),(4,2)],5) => [1] => 10 => 1
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => [2] => 100 => 1
([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) => [2,2] => 1100 => 1
([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => [2,2] => 1100 => 1
([(0,5),(1,5),(4,2),(4,3),(5,4)],6) => [2,2] => 1100 => 1
([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [2] => 100 => 1
([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) => [2,2] => 1100 => 1
([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) => [2,2] => 1100 => 1
([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) => [3] => 1000 => 1
([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => [2] => 100 => 1
([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => [2] => 100 => 1
([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => [2] => 100 => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) => [2,2] => 1100 => 1
([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => [3] => 1000 => 1
([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => [1] => 10 => 1
([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => [3] => 1000 => 1
([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => [2] => 100 => 1
([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) => [3] => 1000 => 1
([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) => [2,2] => 1100 => 1
([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) => [2,2] => 1100 => 1
([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => [2,2] => 1100 => 1
([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) => [2,2] => 1100 => 1
([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => [2] => 100 => 1
([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => [2] => 100 => 1
([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) => [2,2] => 1100 => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) => [2,2] => 1100 => 1
([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => [2] => 100 => 1
([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) => [2,2] => 1100 => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) => [2,2] => 1100 => 1
([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) => [2,2] => 1100 => 1
([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) => [3] => 1000 => 1
([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) => [3] => 1000 => 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) => [2,2] => 1100 => 1
([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => [2] => 100 => 1
([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => [3] => 1000 => 1
([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => [1] => 10 => 1
([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [3] => 1000 => 1
([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) => [3] => 1000 => 1
([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => [2] => 100 => 1
([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) => [2] => 100 => 1
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 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
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
promotion cycle type
Description
The cycle type of promotion on the linear extensions of a poset.