Andrey Kupavskii

The Erdos Matching Conjecture and related questions.

Consider a family of k-element subsets of an n-element set, and assume that the family does not contain s pairwise disjoint sets. The well-known Erdos Matching Conjecture suggests the maximum size of such a family. Finding the maximum is trivial for n2sk. In this work, we improve the bound for any k and large enough s. We also discuss the connection of the problem to an old question on deviations of sums of random variables going back to the work of Hoeffding and Shrikhande.