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SimplesOfProjectiveDimensionAtMostFour on DyckPath ​

The simple modules of projective dimension at most four.

On DyckPath

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

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FindStat St001190

Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra.

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]4
[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/St001190 has the rest.