Regular Intersecting Families
Ferdinand Ihringer, Andrey Kupavskii

TL;DR
This paper studies intersecting families of k-element subsets of an n-set, focusing on their size and element distribution, revealing that such families are small when k grows much slower than n.
Contribution
It characterizes the size and distribution properties of regular intersecting families, especially their asymptotic behavior as n and k vary.
Findings
Intersects families are small when k=o(n).
Distribution of elements in the family is approximately uniform.
Provides bounds on the size of regular intersecting families.
Abstract
We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families of -element subsets of such that every element of lies in the same (or approximately the same) number of members of . In particular, we show that we can guarantee if and only if .
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