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arXiv · 1311.0531

A note on triangulations of sum sets

Karoly J. Boroczky·Benjamin Hoffman
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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.

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Karoly J. Boroczky, Benjamin Hoffman. 2013-11-03. A note on triangulations of sum sets. https://arxiv.org/abs/1311.0531

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