Multicolor Discrepancy of Arithmetic Structures

Bisecting and D-secting families for set systems

“…Then, the discrepancy of the hypergraph G, denoted by disc(G), is defined as disc(G) = min X max e∈E C X (e). For definitions, results, and extensions of discrepancy and related problems, see [9,15,13,7]. Below, we define β D (E) in terms of the discrepancy of a hypergraph G(V, E), where D = [±i].…”

A Panorama of Discrepancy Theory

“…Among the interesting classes of hypergraphs are certainly those with some arithmetic structures, like the hypergraph of arithmetic progressions in the first n integers (Roth [47]; Matoušek and Spencer [35]) and their generalizations, like products and sums of arithmetic progressions (Doerr, Srivastav and Wehr [21]; Hebbinghaus [27]; Přívětivý [45]) or hyperplanes in finite vector spaces (Hebbinghaus, Schoen and Srivastav [28]). …”