ModulesOfMaximalProjectiveAndInjectiveDimension on DyckPath
The indecomposable modules whose projective and injective dimensions both equal the global dimension.
Called as CombinatorialStat(x, "ModulesOfMaximalProjectiveAndInjectiveDimension"). The head's page has its examples.
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FindStat St001001
The number of indecomposable modules with projective and injective dimension equal to the global dimension of the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001001 has the rest.