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InjectivesOfGradeAtLeastTwo on DyckPath ​

The indecomposable injective modules of grade at least two.

On DyckPath

FindStat's St001185.

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

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Distribution

Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.

FindStat St001185

The number of indecomposable injective modules of grade at least two in the linear Nakayama algebra corresponding to a Dyck path.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001185 has the rest.