  By an analogy to the duality between the recurrence time and the longest
match length, we introduce a quantity dual to the maximal repetition length,
which we call the repetition time. Extending prior results, we sandwich the
repetition time in terms of unconditional and conditional min-entropies. The
condition for the upper bound resembles short memory in the sense developed in
time series analysis. Our reasonings make a repeated use of dualities between
so called times and so called counts that generalize the duality of the
recurrence time and the longest match length. We also discuss the analogy of
these results with the Wyner-Ziv/Ornstein-Weiss theorem, which sandwiches the
recurrence time in terms of Shannon entropies. We formulate the respective
sandwich bounds in a way that applies to some cases of a stretched exponential
growth. Such a growth was observed empirically for natural language. However,
our results are too weak to apply to natural language directly because of its
long-memory properties.
