MaximalFirstExtensionWithRegularModule on DyckPath
The greatest dimension of the first extensions of an indecomposable module by the regular module.
FindStat's St001210, over the pairs (v, y) of an indecomposable module as one list: a nested maximum would not evaluate.
Called as CombinatorialStat(x, "MaximalFirstExtensionWithRegularModule"). The head's page has its examples.
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FindStat St001210
Gives the maximal vector space dimension of the first Ext-group between an indecomposable module X and the regular module A, when A is the Nakayama algebra corresponding to the Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 1 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001210 has the rest.