On Sumsets and Convex Hull

@article{Brczky2014OnSA,
  title={On Sumsets and Convex Hull},
  author={K{\'a}roly J. B{\"o}r{\"o}czky and Francisco Santos and Oriol Serra},
  journal={Discrete & Computational Geometry},
  year={2014},
  volume={52},
  pages={705-729}
}
  • Károly J. Böröczky, Francisco Santos, Oriol Serra
  • Published 2014
  • Computer Science, Mathematics
  • Discrete & Computational Geometry
  • One classical result of Freiman gives the optimal lower bound for the cardinality of $$A+A$$A+A if $$A$$A is a $$d$$d-dimensional finite set in $$\mathbb R^d$$Rd. Matolcsi and Ruzsa have recently generalized this lower bound to $$|A+kB|$$|A+kB| if $$B$$B is $$d$$d-dimensional, and $$A$$A is contained in the convex hull of $$B$$B. We characterize the equality case of the Matolcsi–Ruzsa bound. The argument is based partially on understanding triangulations of polytopes. 

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