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- W2963374976 abstract "We study the function $M(n,k)$ which denotes the number of maximal $k$-uniform intersecting families $mathcal{F}subseteq binom{[n]}{k}$. 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 $k$, $M(n,k) =n^{Theta(binom{2k}{k})}$ 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 cross-intersecting system. We also introduce and investigate some related functions and parameters." @default.
- W2963374976 created "2019-07-30" @default.
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- W2963374976 date "2015-03-30" @default.
- W2963374976 modified "2023-10-14" @default.
- W2963374976 title "On the Number of Maximal Intersecting $k$-Uniform Families and Further Applications of Tuza's Set Pair Method" @default.
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- W2963374976 doi "https://doi.org/10.37236/4955" @default.
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