MaximalModuleProjectiveAndInjectiveDimensionSum on DyckPath
The greatest sum of the projective and the injective dimension of an indecomposable module.
Called as CombinatorialStat(x, "MaximalModuleProjectiveAndInjectiveDimensionSum"). 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 St001258
Gives the maximum of injective plus projective dimension of an indecomposable module over the corresponding Nakayama algebra.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 3 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001258 has the rest.