SimplesOfDominantDimensionEqualToGlobalDimension on DyckPath
The simple modules whose dominant dimension is the global dimension.
Called as CombinatorialStat(x, "SimplesOfDominantDimensionEqualToGlobalDimension"). 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 St001159
The number of simple modules of the linear Nakayama algebra corresponding to a Dyck path whose dominant dimension equals the global dimension of the algebra.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 1 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001159 has the rest.