HalfEvenSimpleProjectiveDimensionSum on DyckPath
Half the sum of the projective dimensions of the simple modules that have even projective dimension.
Called as CombinatorialStat(x, "HalfEvenSimpleProjectiveDimensionSum"). 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 St001507
Half the sum of the projective dimensions of the simple modules of the linear Nakayama algebra corresponding to a Dyck path that have even projective dimension.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[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/St001507 has the rest.