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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.

MSC:
60C05 Combinatorial probability
05A18 Partitions of sets
60F05 Central limit and other weak theorems
Software:
OEIS
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