MaximalSimpleProjectiveAndInjectiveDimensionSum on DyckPath

The greatest sum of the projective and the injective dimension of a simple module.

On DyckPath

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

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Sizes 1 to

FindStat St001183

The maximum of $\operatorname{projdim}(S)+\operatorname{injdim}(S)$ over all simple modules $S$ of the linear Nakayama algebra corresponding to a Dyck path.

Object	Value
[1,0]	1
[1,0,1,0]	2
[1,1,0,0]	2
[1,0,1,0,1,0]	3
[1,0,1,1,0,0]	3
[1,1,0,0,1,0]	3
[1,1,0,1,0,0]	2
[1,1,1,0,0,0]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001183 has the rest.