On the size of maximal intersecting families

Abstract

We show that an $n$-uniform maximal intersecting family has size at most $e^{-n^{0.5+o(1)}}{n}^n$. This improves a recent bound by Frankl. The Spread Lemma of Alweiss, Lowett, Wu and Zhang plays an important role in the proof.

arXiv comment20 pages, revised version