Convolution Estimates and Number of Disjoint Partitions

[摘要] Let $X$ be a finite collection of sets. We count the number of ways a disjoint union of $n-1$ subsets in $X$ is a set in $X$, and estimate the number from above by $|X|^{c(n)}$ where $$c(n)=\left(1-\frac{(n-1)\ln (n-1)}{n\ln n} \right)^{-1}.$$ This extend

[学科分类] 离散数学和组合数学

[关键词] Clusters;Disjoint partitions;Hamming cube