InjectivesOfGradeAtLeastOne on DyckPath
The indecomposable injective modules of grade at least one: Hom into the regular module vanishes.
FindStat's St001184. The grade of a module M is the least i with Ext^i(M, A) nonzero.
Called as CombinatorialStat(x, "InjectivesOfGradeAtLeastOne"). The head's page has its examples.
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FindStat St001184
The number of indecomposable injective modules of grade at least one 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] | 2 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001184 has the rest.