DualRegularModuleVanishingExtensionDegrees 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 vanish.

On DyckPath

FindStat's St000954. Ext^i(D(A), A) is Ext^1 of the (i - 1)-th syzygy.

Called as CombinatorialStat(x, "DualRegularModuleVanishingExtensionDegrees"). 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 St000954

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]	0
[1,0,1,0]	1
[1,1,0,0]	0
[1,0,1,0,1,0]	2
[1,0,1,1,0,0]	0
[1,1,0,0,1,0]	0
[1,1,0,1,0,0]	1
[1,1,1,0,0,0]	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000954 has the rest.