Colouring multijoints
Combinatorics
2014-03-26 v1
Abstract
Let L_1, ..., L_d be pairwise disjoint collections of lines in a d-dimensional vector space over some field. If the collections are sufficiently generic we prove that there exists a d-colouring of the set of multijoints J such that for each j, for each line in L_j, the number of points on it of colour j is O(|J|^{1/d}).
Keywords
Cite
@article{arxiv.1403.6449,
title = {Colouring multijoints},
author = {Anthony Carbery and Stefán Ingi Valdimarsson},
journal= {arXiv preprint arXiv:1403.6449},
year = {2014}
}
Comments
We welcome comments on how this result relates to others in discrete geometry