A Note on Projecting the Cubic Lattice

Abstract

It is shown that, given any (n-1)-dimensional lattice L, there is a vector v in Z^n such that the projection of Z^n onto v^perp is arbitrarily close to L. The problem arises in attempting to find the largest cylinder anchored at two points of Z^n and containing no other points of Z^n.

6 pages, 0 figures. Revised Apr 24 2010 because there was an error in the proof of Prop. 3. Revised May 25 2010 because the roles of A and A_v had been swapped in (1) and (3). Revised Jul 14 2010 to clarify choice of basis for projected lattice