  The output of an association rule miner is often huge in practice. This is
why several concise lossless representations have been proposed, such as the
"essential" or "representative" rules. We revisit the algorithm given by
Kryszkiewicz (Int. Symp. Intelligent Data Analysis 2001, Springer-Verlag LNCS
2189, 350-359) for mining representative rules. We show that its output is
sometimes incomplete, due to an oversight in its mathematical validation. We
propose alternative complete generators and we extend the approach to an
existing closure-aware basis similar to, and often smaller than, the
representative rules, namely the basis B*.
