FirstSimpleProjectiveDimension on DyckPath
The projective dimension of the first simple module of the path's linear Nakayama algebra.
FindStat's St001135.
Called as CombinatorialStat(x, "FirstSimpleProjectiveDimension"). The head's page has its examples.
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FindStat St001135
The projective dimension of the first simple module in the Nakayama algebra corresponding to the Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001135 has the rest.