DualRegularModuleFirstExtensionDimension on DyckPath

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

On DyckPath

FindStat's St000951: the dimension of Ext^1(D(A), A). Ext^1 of an interval module is read off the maps from its syzygy and its projective cover.

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

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Distribution

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Sizes 1 to

FindStat St000951

The dimension of $\operatorname{Ext}^{1}(D(A),A)$ for the linear Nakayama algebra corresponding to a Dyck path.

Object	Value
[1,0]	1
[1,0,1,0]	0
[1,1,0,0]	3
[1,0,1,0,1,0]	0
[1,0,1,1,0,0]	2
[1,1,0,0,1,0]	2
[1,1,0,1,0,0]	0
[1,1,1,0,0,0]	6

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000951 has the rest.