RegularModuloSocleToRadicalExtensionDimension on DyckPath
The dimension of the first extensions of the regular module modulo its socle by the Jacobson radical.
FindStat's St001254.
Called as CombinatorialStat(x, "RegularModuloSocleToRadicalExtensionDimension"). The head's page has its examples.
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FindStat St001254
The vector space dimension of the first extension-group between A/soc(A) and J when A is the corresponding Nakayama algebra with Jacobson radical J.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 3 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 4 |
[1,1,0,0,1,0] | 4 |
[1,1,0,1,0,0] | 4 |
[1,1,1,0,0,0] | 6 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001254 has the rest.