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Lattice packings with gap defects are not completely saturated

Greg Kuperberg·Krystyna Kuperberg·Wlodzimierz Kuperberg
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Abstract

We show that a honeycomb circle packing in $\R^2$ 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 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 $\R^3$ with a planar gap defect is also not completely saturated.

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Greg Kuperberg, Krystyna Kuperberg, Wlodzimierz Kuperberg. 2003-03-28. Lattice packings with gap defects are not completely saturated. https://arxiv.org/abs/math/0303366

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