Some Contributions to the Minimum Representation Problem of Key Systems

Some new and improved results on the minimum representation problem for key systems will be presented. By improving a lemma of the second author we obtain better or new results on badly representable key systems, such as showing the most badly representable key system known, namely of size 2n(1−c·loglogn / logn) where n is the number of attributes. We also make an observation on a theorem of J. Demetrovics, Z. Furedi and the first author and give some new well representable key systems as well.