# Joints tightened.

@article{Yu2019JointsT, title={Joints tightened.}, author={Hung-Hsun Hans Yu and Yufei Zhao}, journal={arXiv: Combinatorics}, year={2019} }

In $d$-dimensional space (over any field), given a set of lines, a joint is a point passed through by $d$ lines not all lying in some hyperplane. The joints problem asks to determine the maximum number of joints formed by $L$ lines, and it was one of the successes of the Guth--Katz polynomial method. We prove a new upper bound on the number of joints that matches, up to a $1+o(1)$ factor, the best known construction: place $k$ generic hyperplanes, and use their $(d-1)$-wise intersections to… CONTINUE READING

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