ProjectivesOfDominantDimensionEqualToGlobalDimensionOrInjective on DyckPath
The indecomposable projective modules that are injective or whose dominant dimension is the global dimension.
FindStat's St001166. A projective-injective module has dominant dimension past the global dimension, so the two cases do not overlap.
Called as CombinatorialStat(x, "ProjectivesOfDominantDimensionEqualToGlobalDimensionOrInjective"). The head's page has its examples.
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FindStat St001166
The number of indecomposable projective non-injective modules whose dominant dimension equals the global dimension of the linear Nakayama algebra corresponding to a Dyck path, plus the number of indecomposable projective-injective modules.
| Object | Value |
|---|---|
[1,0] | 2 |
[1,0,1,0] | 3 |
[1,1,0,0] | 3 |
[1,0,1,0,1,0] | 4 |
[1,0,1,1,0,0] | 3 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001166 has the rest.