optimal partition into cartesian products?

I've got a theoretical problem I'm hoping someone can give me a citation
for. I'm trying to partition a subset of a n-dimensional cartesian product
into a miniumum number of cartesian products. For example, if n=2,
A = {a,b,c} and B = {d,e,f}, I might have a subset {ad,bd,be,cd,ce,cf} and
I want to find the minimum # of rectangles needed to tile the triangle
in the diagram below (answer=3). A general solution would of course allow
for arbitrary n and for moving rows and columns around in the diagram.




                                a x
                                b x x
                                c x x x
                                        d e f


Alan Wendt
--

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