Bernoulli numbers and the probability of a birthday surprise
Numerical Analysis
2025-10-20 v4 Numerical Analysis
Number Theory
Optimization and Control
Probability
Abstract
A birthday surprise is the event that, given k uniformly random samples from a sample space of size n, at least two of them are identical. We show that Bernoulli numbers can be used to derive arbitrarily exact bounds on the probability of a birthday surprise. This result can be used in arbitrary precision calculators, and it can be applied to better understand some questions in communication security and pseudorandom number generation.
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Cite
@article{arxiv.math/0304028,
title = {Bernoulli numbers and the probability of a birthday surprise},
author = {Boaz Tsaban},
journal= {arXiv preprint arXiv:math/0304028},
year = {2025}
}
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