On Sumsets and Convex Hull

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 R. 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.

DOI: 10.1007/s00454-014-9633-2

Extracted Key Phrases

Cite this paper

@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} }