Lattice packings with gap defects are not completely saturated
Greg Kuperberg, Krystyna Kuperberg, Wlodzimierz Kuperberg
Abstract
We show that a honeycomb circle packing in 2 with a linear gap defect cannot be completely saturated, no matter how narrow the gap is. The result is motivated by an open problem of G. Fejes Tóth, G. Kuperberg, and W. Kuperberg, which asks whether of a honeycomb circle packing with a linear shift defect is completely saturated. We also show that an fcc sphere packing in 3 with a planar gap defect is also not completely saturated.
Create a lesson
Related papers
Each simplex in R4 has a point with at least 14 emanating normals to its boundary
Ivan Nasonov, Gaiane Panina
Pointed Gromov-Hausdorff Distance between lp-Wedge Sums and Isometric Embeddings of l∞
Emin Abdullaev
Embedding large subsets of Wasserstein spaces into Banach spaces
Cyril Letrouit, Quentin Mérigot
A Smooth Covariogram and the Transition Between Projection Bodies
J. Haddad, C. H. Jiménez, M. Resende Guedes
Intermediate coverings, random images, and projections
Yunhao Zhao, Yingyu Zhao, Chen Zhou et al.
On the Graph Corresponding to Center of Distances of Metric Space
Oleksiy Dovgoshey, Olga Rovenska