RegularModuleSecondInjectiveTermProjectiveDimension on DyckPath
The greatest projective dimension of the second term of the minimal injective coresolution of an indecomposable projective module.
FindStat's St001273, which calls this the first term: its rows count the injective hull as the zeroth term, the injective hull of the first cosyzygy as the first.
Called as CombinatorialStat(x, "RegularModuleSecondInjectiveTermProjectiveDimension"). The head's page has its examples.
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FindStat St001273
The projective dimension of the first term in an injective coresolution of the regular module.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001273 has the rest.