Colouring multijoints
Abstract
Let L1, ..., Ld 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 Lj, the number of points on it of colour j is O(|J|1/d).
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