Central Limit Theorems for some Set Partition Statistics
classification
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math.PR
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centrallimitnumberpartitionprovetheoremsargumentschosen
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We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = {1,2,...,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.
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