On lines, joints, and incidences in three dimensions
Journal of Combinatorial Theory Series A
Computing the distance between piecewise-linear bivariate functions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We show that given a collection of $A$ lines in $\mathbb{R}^n$, $n\geq2$, the maximum number of their joints (points incident to at least $n$ lines whose directions form a linearly independent set) is $O(A^{n/(n-1)})$. An analogous result for smooth algebraic curves is also proven.