NakayamaFinitisticDominantDimension on DyckPath
The greatest finite dominant dimension of an indecomposable module.
FindStat's St000686. A dominant dimension reaching the vertex count is the infinite one the fold caps at.
Called as CombinatorialStat(x, "NakayamaFinitisticDominantDimension"). The head's page has its examples.
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Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St000686
The finitistic dominant dimension of 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] | 2 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000686 has the rest.