SimplesOfInjectiveDimensionEqualToDominantDimension on DyckPath
The simple modules whose injective dimension equals their dominant dimension.
FindStat's St001028, read with the dominant dimension of the module itself: that is the reading its rows follow.
Called as CombinatorialStat(x, "SimplesOfInjectiveDimensionEqualToDominantDimension"). The head's page has its examples.
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FindStat St001028
The number of simple modules with injective dimension equal to the dominant dimension in the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 2 |
[1,0,1,0] | 3 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 4 |
[1,0,1,1,0,0] | 3 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001028 has the rest.