SecondToLastInjectiveProjectiveDimension on DyckPath
The projective dimension of the indecomposable injective module whose socle is the second-to-last simple module.
FindStat's St001217, I[n-2] with the simples numbered 0 to n-1.
Called as CombinatorialStat(x, "SecondToLastInjectiveProjectiveDimension"). The head's page has its examples.
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FindStat St001217
The projective dimension of the indecomposable injective module I[n-2] in the corresponding Nakayama algebra with simples enumerated from 0 to n-1.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001217 has the rest.