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- W4212963909 abstract "We consider the problem where p players aim independently to a complete set of N different types of items (species, viruses) which are uniformly distributed. Let the random variables T N ( i ) , i = 1 , 2 , … , p denoting the number of trials needed until all N types are detected (at least once), respectively for each player. This paper studies the impact of the number p in the asymptotics of the expectation, the second moment, and the variance of the random variable M N ( p ) : = ⋀ i = 1 p T N ( i ) , N → ∞ . The main ingredient in the expression of these quantities are sums involving the Stirling numbers of the second kind; for which the asymptotics are explored. At the end of the paper we conjecture on a remarkable identity, regarding alternating binomial sums. These sums have been studied (mainly) by P. Flajolet due to their applications to digital search trees and quadtrees." @default.
- W4212963909 created "2022-02-24" @default.
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- W4212963909 date "2022-06-01" @default.
- W4212963909 modified "2023-09-27" @default.
- W4212963909 title "On the minimum of independent collecting processes via the Stirling numbers of the second kind" @default.
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- W4212963909 doi "https://doi.org/10.1016/j.spl.2022.109426" @default.
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