SimplesOfVanishingSecondExtensionWithRegularModule on DyckPath
The simple modules with no second extension by the regular module.
FindStat's St001211.
Called as CombinatorialStat(x, "SimplesOfVanishingSecondExtensionWithRegularModule"). The head's page has its examples.
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FindStat St001211
The number of simple modules in the corresponding Nakayama algebra that have vanishing second Ext-group with the regular module.
| Object | Value |
|---|---|
[1,0] | 2 |
[1,0,1,0] | 2 |
[1,1,0,0] | 3 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 3 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001211 has the rest.