SimpleProjectiveDimensionProduct on DyckPath

The product of the nonzero projective dimensions of the simple modules of the path's linear Nakayama algebra.

On DyckPath

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

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Sizes 1 to

FindStat St001299

The product of all nonzero projective dimensions of simple modules of the linear Nakayama algebra corresponding to a Dyck path.

Object	Value
[1,0]	1
[1,0,1,0]	2
[1,1,0,0]	1
[1,0,1,0,1,0]	6
[1,0,1,1,0,0]	2
[1,1,0,0,1,0]	2
[1,1,0,1,0,0]	2
[1,1,1,0,0,0]	1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001299 has the rest.