The set system of all arithmetic progressions on [n] is known to have a discrepancy of order n1/4. We investigate the discrepancy for the set system S3 n formed by all sums of three arithmetic… (More)

Given a graph G = (V,E) with n vertices, m edges and maximum vertex degree ∆, the load distribution of a coloring φ : V → {red, blue} is a pair dφ = (rφ, bφ), where rφ is the number of edges with at… (More)

Let A be an n-point set in the plane. A discrete X-ray of A in direction u gives the number of points of A on each line parallel to u. We define F(k) as the maximum number n such that there exist k… (More)

Let Dd n denote the d-dimensional grid with diagonals, that is, the graph with vertex set {1, 2, . . . , n}d and with edges connecting every two vertices that differ by at most 1 in every coordinate.… (More)