SimplesOfNonVanishingSecondExtensionWithRegularModule on DyckPath
The simple modules with a nonzero second extension by the regular module.
FindStat's St001212.
Called as CombinatorialStat(x, "SimplesOfNonVanishingSecondExtensionWithRegularModule"). The head's page has its examples.
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FindStat St001212
The number of simple modules in the corresponding Nakayama algebra that have non-zero second Ext-group 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] | 1 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001212 has the rest.