DualRegularModuleNonVanishingExtensionDegrees on DyckPath

The degrees i from 1 to the global dimension at which the extensions of the direct sum of the indecomposable injective modules by the regular module do not vanish.

On DyckPath

FindStat's St000955.

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

Live

Distribution

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

Sizes 1 to

FindStat St000955

The number of integers $i > 0$ such that $\operatorname{Ext}^i(D(A),A) > 0$ for the linear Nakayama algebra corresponding to a Dyck path.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000955 has the rest.