other block designs

[Leonard Soicher]

On Tue, Sep 23, 2003 at 06:39:34PM -0400, John P. Morgan wrote:
> Dear All,
> 
> This note outlines some important examples of block designs that we cannot
> currently accomodate.  There are other, equivalent combinatorial objects for
> some of the four examples listed which are not mentioned.  A common theme for
> the four examples is given.
> 
[...]

As JP has pointed out wery well, many designs are block designs
with some additional structure. This may be structure on the 
point set, the block multiset, or on the the blocks themselves.

Each time we impose additional structure then the definition of certain
notions, including isomorphism and automorphism group, may change,
as well as new properties being of interest that are not of interest 
or don't make sense for basic block designs.

This is an argument for considering block designs with some specific
extra structure to be treated as a new class of designs.  We may want to
store the "underlying" block design for such a design and the properties
of this underlying block design using the current block design ext-rep,
and then additionally store new properties and properties having a
different interpretation for the new class of design.

I believe we will get into a great deal of trouble if we try to tweak
our current block design ext-rep to handle extra structure on top of
the block design. 

Leonard