partial balance

[John P. Morgan]

Dear All,

This is a recommendation that the discussion of partial_balance_properties in 
ext-rep.txt include some statistical context in addition to what has so far been 
written (don't know who is working on this section, but am happy to discuss 
off-line as well). Something along the lines of:

Partial balance of a block design d can also be defined in terms of its 
information matrix C_d (as defined in the section Statistical Properties below), 
though ``partial_balance_properties`` has not been included under 
``statistical_properties`` due to its considerable interest from other 
perspectives. The pairwise variances v_{dxy} induced by a partially balanced 
design depend only on the association between x and y. Thus if d is partially 
balanced with s associate classes, it admits at most s values for v_{dxy}. This 
is the genesis of the "partially balanced" notion.

The above is not necessary for the definition of partial_balance_properties, but 
neither is the material explaining how a balancing scheme can be found from the 
automorphism group. Rather, both are basic information about the concept and its 
relation to other categories in the external rep.


JP