The Bottleneck Birthday Problem asks for the maximum group size keeping the probability that no day receives more than r birthdays at or above 1/2, solved via new recurrences that combine occupancy methods with restricted Stirling numbers of the second kind.
The matching, birthday and the strong birthday problem: a contemporary review.Journal of Statistical Planning and Inference, 130(1-2):377–389
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The Bottleneck Birthday Problem
The Bottleneck Birthday Problem asks for the maximum group size keeping the probability that no day receives more than r birthdays at or above 1/2, solved via new recurrences that combine occupancy methods with restricted Stirling numbers of the second kind.