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Ting-Wei Chao (趙庭偉), Tight Bound on Joints Problem and Partial Shadow Problem
Ting-Wei Chao (趙庭偉), Tight Bound on Joints Problem and Partial Shadow Problem
Given a set of lines in $\mathbb R^d$, a joint is a point contained in d linearly independent lines. Guth and Katz showed that N lines can determine at most $O(N^{3/2})$ joints in $\mathbb R^3$ via the polynomial method. Yu and I proved a tight bound on this problem, which also solves a conjecture proposed …