Skip to content

ProjectiveSquaredRadicalsOfInjectiveDimensionAtMostOne on DyckPath ​

The indecomposable projective modules whose square radical, zero included, has injective dimension at most one.

On DyckPath

FindStat's St001240: the modules e_i J^2, the zero ones included.

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

Live

Distribution

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

FindStat St001240

The number of indecomposable modules e_i J^2 that have injective dimension at most one in the corresponding Nakayama algebra

The number of indecomposable modules e_i J^2 that have injective dimension at most one 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]3
[1,1,1,0,0,0]4

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001240 has the rest.