InjectivesOfNonMaximalSocleProjectiveDimensionMinusProjectiveInjectives on DyckPath
The indecomposable injective modules whose socle has projective dimension less than the global dimension, less the indecomposable projective-injective modules.
FindStat's St001164. An indecomposable projective is injective when the one before it is no longer than it.
Called as CombinatorialStat(x, "InjectivesOfNonMaximalSocleProjectiveDimensionMinusProjectiveInjectives"). The head's page has its examples.
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FindStat St001164
The number of indecomposable injective modules whose socle has projective dimension at most the global dimension of the algebra minus one of the linear Nakayama algebra corresponding to a Dyck path, minus the number of indecomposable projective-injective modules.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[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] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001164 has the rest.