  In the context of mining for frequent patterns using the standard levelwise
algorithm, the following question arises: given the current level and the
current set of frequent patterns, what is the maximal number of candidate
patterns that can be generated on the next level? We answer this question by
providing a tight upper bound, derived from a combinatorial result from the
sixties by Kruskal and Katona. Our result is useful to reduce the number of
database scans.
