LastSimpleOfMaximalProjectiveDimension on DyckPath
The last vertex, counting from 0, whose simple module has projective dimension equal to the global dimension.
Called as CombinatorialStat(x, "LastSimpleOfMaximalProjectiveDimension"). The head's page has its examples.
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FindStat St001265
The maximal i such that the i-th simple module has projective dimension equal to the global dimension in the corresponding Nakayama algebra.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[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] | 0 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001265 has the rest.