Abstract
We study the asymptotic behavior of the maximal multiplicity μ n = μ n (λ) of the parts in a partition λ of the positive integer n, assuming that λ is chosen uniformly at random from the set of all such partitions. We prove that πμ n /(6n)1/2 converges weakly to max j X j /j as n→∞, where X1, X2, … are independent and exponentially distributed random variables with common mean equal to 1.
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2000 Mathematics Subject Classification: Primary—05A17; Secondary—11P82, 60C05, 60F05
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Mutafchiev, L.R. On the Maximal Multiplicity of Parts in a Random Integer Partition. Ramanujan J 9, 305–316 (2005). https://doi.org/10.1007/s11139-005-1870-9
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DOI: https://doi.org/10.1007/s11139-005-1870-9