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- W4226480382 abstract "We prove that the number of tangencies between the members of two families, each of which consists of $n$ pairwise disjoint curves, can be as large as $Omega(n^{4/3})$. We show that from a conjecture about forbidden $0$-$1$ matrices it would follow that this bound is sharp for doubly-grounded families. We also show that if the curves are required to be $x$-monotone, then the maximum number of tangencies is $Theta(nlog n)$, which improves a result by Pach, Suk, and Treml. Finally, we also improve the best known bound on the number of tangencies between the members of a family of at most $t$-intersecting curves." @default.
- W4226480382 created "2022-05-05" @default.
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- W4226480382 date "2021-11-16" @default.
- W4226480382 modified "2023-10-17" @default.
- W4226480382 title "The number of tangencies between two families of curves" @default.
- W4226480382 doi "https://doi.org/10.48550/arxiv.2111.08787" @default.
- W4226480382 hasPublicationYear "2021" @default.
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