In this paper, we determine the largest family $\mathcal F \subset 2^{[n]}$ without $s$ pairwise disjoint sets, provided $n=ms+c$ for positive integers $m,c$, and $s \geq s_0(m, c)$. This result can be seen as a non-uniform analogue of the results on the Erd\H os Matching Conjecture in the regime when the clique is extremal.

翻译：本文确定了当$n=ms+c$（$m,c$为正整数）且$s \geq s_0(m, c)$时，不含$s$个两两不交集合的最大族$\mathcal F \subset 2^{[n]}$。该结果可视为在团为极值情形下，关于Erdős匹配猜想结论的非均匀类似物。