When is the ball a local pessimum for covering?
classification
🧮 math.MG
math.FA
keywords
coveringdimensionsballpessimumlatticelocalpoint-symmetricballs
read the original abstract
We consider the problem of identifying the worst point-symmetric shape for covering n-dimensional Euclidean space with lattice translates. Here we focus on the dimensions where the thinnest lattice covering with balls is known and ask whether the ball is a pessimum for covering in these dimensions compared to all point-symmetric convex shapes. We find that the ball is a local pessimum in 3 dimensions, but not so for 4 and 5 dimensions.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.