FirstSimpleOfMaximalProjectiveDimension on DyckPath
The first vertex, counting from 0, whose simple module has projective dimension equal to the global dimension.
Called as CombinatorialStat(x, "FirstSimpleOfMaximalProjectiveDimension"). 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 St001264
The smallest index i such that the i-th simple module has projective dimension equal to the global dimension of the corresponding Nakayama algebra.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001264 has the rest.