We study four problems: put n distinguishable/non-distinguishable balls into k non-empty distinguishable/non-distinguishable boxes randomly. What is the threshold function k = k(n) to make almost sure that no two boxes contain the same number of balls The non-distinguishable ball problems are very close to the Erdos-Lehner asymptotic formula for the number of partitions of the integer n into k parts with k = o(n 1/3). The problem is motivated by the statistics of an experiment, where we only can tell whether outcomes are identical or different. © Springer-Verlag Berlin Heidelberg 2013.
CITATION STYLE
Czabarka, É., Marsili, M., & Székely, L. A. (2013). Threshold functions for distinct parts: Revisiting Erdos-Lehner. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7777, pp. 463–471). Springer Verlag. https://doi.org/10.1007/978-3-642-36899-8_22
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