The joints problem in R^n
Combinatorics
2009-06-15 v3
Abstract
We show that given a collection of A lines in \R^n, n\geq 2, 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.
Cite
@article{arxiv.0906.0555,
title = {The joints problem in R^n},
author = {René Quilodrán},
journal= {arXiv preprint arXiv:0906.0555},
year = {2009}
}
Comments
6 pages, removed erroneous argument that appeared in version 2 about incidences