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RadicalToSquaredRadicalExtensionDimension on DyckPath ​

The dimension of the first extensions of the Jacobson radical by its square.

On DyckPath

FindStat's St001229.

Called as CombinatorialStat(x, "RadicalToSquaredRadicalExtensionDimension"). The head's page has its examples.

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FindStat St001229

The vector space dimension of the first extension group between the Jacobson radical J and J^2.

ObjectValue
[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]0
[1,1,0,0,1,0]0
[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/St001229 has the rest.