Alon and Furedi determined the minimum number of affine hyperplanes needed to cover all but one vertex of an $n$-cube. We extend this question to the case where all vertices must be covered at least k times, except for one which is not covered at all. Using the Punctured Combinatorial Nullstellensatz of Ball and Serra, we solve the problem completely for $k=3$ and establish a nontrivial lower bound when k>3. Time permitting, we will also discuss this problem for more general grids, including an exact solution for k=2.
Joint work with Hao Huang.
For Zoom information, please contact Sean at SEnglish (at) illinois (dot) edu
