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Most Downloaded Articles
- The cyclic q-clans with q = 2 e by Cherowitzo, William E. and Payne, Stanley E.
- Quasigeodesics and farthest points on convex surfaces by Ieiri, K./ Itoh, J. and Vîlcu, C.
- Transversal numbers over subsets of linear spaces by Averkov, G. and Weismantel, R.
- Manifolds with large isotropy groups by Kollross, Andreas and Samiou, Evangelia
- Manifolds with asymptotically nonnegative minimal radial curvature by Santos, Newton L
Free Planes in Lattice Sphere Packings
Citation Information: Advances in Geometry. Volume 5, Issue 1, Pages 137–144, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: 10.1515/advg.2005.5.1.137, July 2005
- 6 October, 2003
- 12 February, 2004
- Published Online:
We show that for every lattice packing of n-dimensional spheres there exists an (n/log2(n))-dimensional affine plane which does not meet any of the spheres in their interior, provided n is large enough. Such an affine plane is called a free plane and our result improves on former bounds.