SimplesOfOneDimensionalSecondExtensionWithRegularModule on DyckPath
The simple modules whose second extensions by the regular module have dimension one.
FindStat's St001222.
Called as CombinatorialStat(x, "SimplesOfOneDimensionalSecondExtensionWithRegularModule"). The head's page has its examples.
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FindStat St001222
Number of simple modules in the corresponding LNakayama algebra that have a unique 2-extension with the regular module.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[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] | 0 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001222 has the rest.