SimplesOfMaximalProjectiveDimension on DyckPath
The simple modules whose projective dimension is the global dimension.
Called as CombinatorialStat(x, "SimplesOfMaximalProjectiveDimension"). The head's page has its examples.
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FindStat St001006
The number of simple modules with projective dimension equal to the global dimension of the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 1 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001006 has the rest.