A tight upper bound on the number of candidate patterns

In the context of mining for frequent patterns using the standard level-wise 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 by J. Kruskal (1963) and G. Katona (1968). Our result is useful for reducing the number of database scans.