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SimplesOfDominantDimensionAtLeastThree on DyckPath ​

The simple modules whose dominant dimension is at least three.

On DyckPath

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

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FindStat St001163

The number of simple modules of dominant dimension at least three in the linear Nakayama algebra corresponding to a Dyck path.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001163 has the rest.