OneRegularSimpleModules on DyckPath
The simple modules of projective dimension one, grade one and one-dimensional first extension by the regular module.
FindStat's St001126. A simple module is k-regular when its projective dimension is k, Ext^k(S, A) is one-dimensional and Ext^i(S, A) vanishes below k.
Called as CombinatorialStat(x, "OneRegularSimpleModules"). 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 St001126
The number of 1-regular simple modules of the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 0 |
[1,1,0,0] | 2 |
[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] | 1 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001126 has the rest.