Combinatorics Seminar: "Almost k-covers of grids"

Abstract: Alon and Füredi 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.

Host: Adeli Hutton, Martha Precup, and Laura Vega