ProjectivesOfInjectiveDimensionAtMostDominantDimension on DyckPath
The indecomposable projective modules whose injective dimension is at most their dominant dimension.
FindStat's St000998, read with the dominant dimension of the module itself: that is the reading its rows follow.
Called as CombinatorialStat(x, "ProjectivesOfInjectiveDimensionAtMostDominantDimension"). The head's page has its examples.
Live
Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St000998
The number of indecomposable projective modules with injective dimension less than or 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] | 3 |
[1,0,1,0,1,0] | 4 |
[1,0,1,1,0,0] | 4 |
[1,1,0,0,1,0] | 4 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000998 has the rest.