On the number of maximal intersecting k-uniform families and further applications of Tuza's set pair method

We study the function M(n, k) which denotes the number of maximal k-uniform intersecting families F subset of (([n])(k)). Improving a bound of Balogh, Das, Delcourt, Liu and Sharifzadeh on M(n, k), we determine the order of magnitude of log M(n, k) by proving that for any fixed k, M(n, k) = n Theta(((2K))) holds. Our proof is based on Tuza's set pair approach. The main idea is to bound the size of the largest possible point set of a crossintersecting system. We also introduce and investigate some related functions and parameters.