DualRegularModuleTopExtensionDimension on DyckPath

The dimension of the extensions in the global dimension of the direct sum of the indecomposable injective modules by the regular module.

On DyckPath

FindStat's St000964.

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

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Distribution

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

Sizes 1 to

FindStat St000964

The dimension of $\operatorname{Ext}^g(D(A),A)$ for the linear Nakayama algebra corresponding to a Dyck path, where $g$ is the global dimension of that algebra.

Object	Value
[1,0]	1
[1,0,1,0]	1
[1,1,0,0]	3
[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]	3
[1,1,1,0,0,0]	6

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000964 has the rest.