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SimplesOfSmallInjectiveDimensionOrPositiveDominantDimension on DyckPath ​

The simple modules whose injective dimension is at most one or whose dominant dimension is at least one.

On DyckPath

Called as CombinatorialStat(x, "SimplesOfSmallInjectiveDimensionOrPositiveDominantDimension"). 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 St001237

The number of simple modules with injective dimension at most one or dominant dimension at least one.

ObjectValue
[1,0]2
[1,0,1,0]3
[1,1,0,0]3
[1,0,1,0,1,0]4
[1,0,1,1,0,0]4
[1,1,0,0,1,0]3
[1,1,0,1,0,0]4
[1,1,1,0,0,0]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001237 has the rest.