SimpleSummandsOfSecondRadicalLayer on DyckPath

The simple summands of J^2/J^3 for the Jacobson radical J of the path's linear Nakayama algebra, one for each indecomposable projective of dimension at least three.

On DyckPath

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

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Sizes 1 to

FindStat St001480

The number of simple summands of the module $J^2/J^3$ in the linear Nakayama algebra corresponding to a Dyck path.

Object	Value
[1,0,1,0]	0
[1,1,0,0]	1
[1,0,1,0,1,0]	0
[1,0,1,1,0,0]	1
[1,1,0,0,1,0]	1
[1,1,0,1,0,0]	2
[1,1,1,0,0,0]	2
[1,0,1,0,1,0,1,0]	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001480 has the rest.