ProjectiveMinusCodominantDimensionSum on DyckPath
The sum, over the non-projective indecomposable injective modules, of their projective dimension less their codominant dimension.
Called as CombinatorialStat(x, "ProjectiveMinusCodominantDimensionSum"). The head's page has its examples.
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FindStat St001021
The sum of the differences between the projective and codominant dimensions of the non-projective indecomposable injective modules of the linear Nakayama algebra corresponding to a Dyck path.
| 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] | 0 |
[1,1,0,0,1,0] | 0 |
[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/St001021 has the rest.