ModulesOfProjectiveDimensionTwo on DyckPath
The indecomposable modules of projective dimension two.
FindStat's St001232 is stated, and crawled, only for algebras of global dimension at most two; the count is the same definition on every path.
Called as CombinatorialStat(x, "ModulesOfProjectiveDimensionTwo"). The head's page has its examples.
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FindStat St001232
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[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] | 0 |
[1,0,1,1,0,0,1,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001232 has the rest.