On sumsets and convex hull
Combinatorics
2016-02-08 v1 Number Theory
Abstract
One classical result of Freimann gives the optimal lower bound for the cardinality of A+A if A is a d-dimensional finite set in the Euclidean d-space. 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.
Keywords
Cite
@article{arxiv.1307.6316,
title = {On sumsets and convex hull},
author = {Karoly Boroczky and Francisco Santos and Oriol Serra},
journal= {arXiv preprint arXiv:1307.6316},
year = {2016}
}