SocleToRadicalExtensionDimension on DyckPath
The dimension of the first extensions of the socle of the regular module by the Jacobson radical.
FindStat's St001227.
Called as CombinatorialStat(x, "SocleToRadicalExtensionDimension"). The head's page has its examples.
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FindStat St001227
The vector space dimension of the first extension group between the socle of the regular module and the Jacobson radical of the corresponding Nakayama algebra.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 2 |
[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/St001227 has the rest.