中文

Lattice packings with gap defects are not completely saturated

度量几何 2019-09-16 v1

摘要

We show that a honeycomb circle packing in R2\R^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 T\'oth, 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 R3\R^3 with a planar gap defect is also not completely saturated.

引用

@article{arxiv.math/0303366,
  title  = {Lattice packings with gap defects are not completely saturated},
  author = {Greg Kuperberg and Krystyna Kuperberg and Wlodzimierz Kuperberg},
  journal= {arXiv preprint arXiv:math/0303366},
  year   = {2019}
}