Discrepancy with respect to convex polygons

We study the problem of discrepancy of finite point sets in the unit square with respect to convex polygons, when the directions of the edges are fixed, when the number of edges is bounded, as well as when no such restrictions are imposed. In all three cases, we obtain estimates for the supremum norm that are very close to best possible.

• Type: Journal
• Year: 2007
• Where: JC
• Authors: W. W. L. Chen, G. Travaglini
• Keywords: JC 2007, Polygons, finite Point Sets