SimplesOfMaximalEvenProjectiveDimension on DyckPath
The simple modules whose projective dimension is the greatest even one that occurs: the global dimension if it is even, else one less.
Called as CombinatorialStat(x, "SimplesOfMaximalEvenProjectiveDimension"). The head's page has its examples.
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FindStat St001493
The number of simple modules whose projective dimension is even and is maximal among the even projective dimensions occurring for simple modules of the linear Nakayama algebra corresponding to a Dyck path.
| 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] | 1 |
[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/St001493 has the rest.