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Central limit theorems for some set partition statistics. (English) Zbl 1327.60030
Summary: We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of \([n] = \{1, 2, \dots, n \}\). The arguments use a novel stochastic representation and are also used to prove central limit theorems for the dimension index and the number of levels.

60C05 Combinatorial probability
05A18 Partitions of sets
60F05 Central limit and other weak theorems
Full Text: DOI arXiv
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