On sumsets and convex hull
Abstract
One classical result of Freimann gives the optimal lower bound for the cardinality of A+A if A is a ddimensional finite set in the Euclidean dspace. Matolcsi and Ruzsa have recently generalized this lower bound to A+kB if B is ddimensional, and A is contained in the convex hull of B. We characterize the equality case of the MatolcsiRuzsa bound. The argument is based partially on understanding triangulations of polytopes.
 Publication:

arXiv eprints
 Pub Date:
 July 2013
 arXiv:
 arXiv:1307.6316
 Bibcode:
 2013arXiv1307.6316B
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Number Theory
 EPrint:
 Discrete Comput. Geom., 52:4, (December 2014), 705729