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InjectivesOfProjectiveDimensionAtMostOne on DyckPath ​

The indecomposable injective modules of projective dimension at most one.

On DyckPath

Called as CombinatorialStat(x, "InjectivesOfProjectiveDimensionAtMostOne"). The head's page has its examples.

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FindStat St001180

The number of indecomposable injective modules with projective dimension at most one of the linear Nakayama algebra corresponding to a Dyck path.

ObjectValue
[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]2
[1,1,1,0,0,0]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001180 has the rest.