Piercing theorems for discrete boxes

Abstract: For a finite family of nonempty sets, the piercing number \tau is the minimum number of points meeting every member, while the packing number \nu is the maximum size of a pairwise disjoint subfamily. We will introduce classical and recent bounds relating these parameters for axis-parallel boxes. We will then consider discrete boxes, obtained by intersecting boxes in R^d with a prescribed point set P. After briefly recalling general piercing results for discrete boxes, we will focus on the planar case and prove the bound \tau = O(\nu \log \nu), with a constant independent of P.

mathematical physicsalgebraic geometryalgebraic topologygeometric topologyquantum algebra

Audience: researchers in the topic

Moscow-Beijing topology seminar

Series comments: https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1h.. Meeting ID: 818 6674 5751 Passcode: 141592