NakayamaDominantDimension on DyckPath
The dominant dimension of the path's linear Nakayama algebra.
FindStat's St000685. An algebra and its opposite have the same dominant dimension, which for the opposite is the least codominant dimension of a non-projective indecomposable injective module.
Called as CombinatorialStat(x, "NakayamaDominantDimension"). 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 St000685
The dominant dimension of the linear Nakayama algebra corresponding to a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 3 |
[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] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000685 has the rest.