A note on triangulations of sum sets
Number Theory
2013-11-05 v1
Abstract
For finite sets A and B in the plane, we write A+B to denote the set of sums of the elements of A and B. In addition, we write tr(A) to denote the common number of triangles in any triangulation of the convex hull of A using the points of A as vertices. We consider the conjecture that tr(A+B)^{1/2}\geq tr(A)^{1/2}+tr(B)^{1/2}. If true, this conjecture would be a discrete, two-dimensional analogue to the Brunn-Minkowski inequality. We prove the conjecture in three special cases.
Keywords
Cite
@article{arxiv.1311.0531,
title = {A note on triangulations of sum sets},
author = {Karoly J. Boroczky and Benjamin Hoffman},
journal= {arXiv preprint arXiv:1311.0531},
year = {2013}
}