SimplesOfEqualProjectiveAndInjectiveDimension on DyckPath
The simple modules whose projective dimension equals their injective dimension.
Called as CombinatorialStat(x, "SimplesOfEqualProjectiveAndInjectiveDimension"). 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 St001027
The number of simple modules with projective dimension equal to injective dimension in the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001027 has the rest.