3 papers
math.CO2025
Improved lower bound for hypercube edge slicing
Lisa Sauermann, Zixuan Xu
How many hyperplanes in are needed in order to slice every edge of the -dimensional hypercube with vertex set ? Here, we say that a hyperplane $H\sub…
math.CO2025
Nondegenerate hyperplane covers of the hypercube
Lisa Sauermann, Zixuan Xu
We consider collections of hyperplanes in covering all vertices of the -dimensional hypercube , which satisfy the following nondegeneracy condition: Fo…
math.CO2023
Essential covers of the hypercube require many hyperplanes
Lisa Sauermann, Zixuan Xu
We prove a new lower bound for the almost 20 year old problem of determining the smallest possible size of an essential cover of the -dimensional hypercube , i.e. t…