ModulesOfProjectiveAndInjectiveDimensionAtMostOne on DyckPath
The indecomposable modules whose projective and injective dimensions are both at most one.
Called as CombinatorialStat(x, "ModulesOfProjectiveAndInjectiveDimensionAtMostOne"). 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.
FindStat St001002
The number of indecomposable modules with projective and injective dimension at most one in the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 3 |
[1,0,1,0] | 3 |
[1,1,0,0] | 6 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 5 |
[1,1,0,0,1,0] | 5 |
[1,1,0,1,0,0] | 5 |
[1,1,1,0,0,0] | 10 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001002 has the rest.