InjectivesOfCodominantDimensionEqualToGlobalDimension on DyckPath
The indecomposable injective modules whose codominant dimension is the global dimension.
A projective-injective module has infinite codominant dimension, so it is never counted.
Called as CombinatorialStat(x, "InjectivesOfCodominantDimensionEqualToGlobalDimension"). The head's page has its examples.
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FindStat St001013
The number of indecomposable injective modules with codominant dimension equal to the global dimension in the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 1 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001013 has the rest.