A Note on Projecting the Cubic Lattice

It is shown that, given any (n−1)-dimensional lattice Λ, there is a vector v∈ℤn such that the orthogonal projection of ℤn onto v⊥ is, up to a similarity, arbitrarily close to Λ. The problem arises in attempting to find the largest cylinder anchored at two points of ℤn and containing no other points of ℤn.

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