ModulesOfVanishingFirstExtensionWithRegularModule on DyckPath
The indecomposable modules with no first extension by the regular module.
FindStat's St001213. Every indecomposable module is (top v - 1, length 1 .. the series' entry at v).
Called as CombinatorialStat(x, "ModulesOfVanishingFirstExtensionWithRegularModule"). The head's page has its examples.
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FindStat St001213
The number of indecomposable modules in the corresponding Nakayama algebra that have vanishing first Ext-group with the regular module.
| Object | Value |
|---|---|
[1,0] | 2 |
[1,0,1,0] | 4 |
[1,1,0,0] | 3 |
[1,0,1,0,1,0] | 6 |
[1,0,1,1,0,0] | 5 |
[1,1,0,0,1,0] | 5 |
[1,1,0,1,0,0] | 6 |
[1,1,1,0,0,0] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001213 has the rest.