SimplesOfGradeAtLeastGlobalDimension on DyckPath

The simple modules of grade at least the global dimension: their extensions with the regular module vanish below it.

On DyckPath

FindStat's St001191.

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

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Sizes 1 to

FindStat St001191

Number of simple modules $S$ with $Ext_A^i(S,A)=0$ for all $i=0,1,...,g-1$ in the corresponding Nakayama algebra $A$ with global dimension $g$.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001191 has the rest.