NakayamaGlobalMinusDominantDimension on DyckPath
The global dimension less the dominant dimension of the path's linear Nakayama algebra.
Called as CombinatorialStat(x, "NakayamaGlobalMinusDominantDimension"). The head's page has its examples.
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FindStat St000688
The global dimension minus the dominant dimension of the linear Nakayama algebra corresponding to a Dyck path.
The global dimension minus the dominant dimension of the linear Nakayama algebra corresponding to a Dyck path. The global dimension is given by St000684 and the dominant dimension is given by St000685. The correspondence between linear Nakayama algebras and Dyck paths is also explained on the [[https://www.findstat.org/CollectionsDatabase/DyckPaths/NakayamaAlgebras/|Nakayama algebras]] pa…
| 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] | 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/St000688 has the rest.