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- Title
On Sumsets and Convex Hull.
- Authors
Böröczky, Károly; Santos, Francisco; Serra, Oriol
- Abstract
One classical result of Freiman gives the optimal lower bound for the cardinality of $$A+A$$ if $$A$$ is a $$d$$ -dimensional finite set in $$\mathbb R^d$$ . Matolcsi and Ruzsa have recently generalized this lower bound to $$|A+kB|$$ if $$B$$ is $$d$$ -dimensional, and $$A$$ is contained in the convex hull of $$B$$ . We characterize the equality case of the Matolcsi-Ruzsa bound. The argument is based partially on understanding triangulations of polytopes.
- Subjects
POLYTOPES; MATHEMATICAL formulas; CARDINAL numbers; VECTORS in N-dimensions; VECTOR algebra
- Publication
Discrete & Computational Geometry, 2014, Vol 52, Issue 4, p705
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-014-9633-2