Abstract: For a set A of points in the plane, not all collinear, we denote by tr(A) the number of triangles in a triangulation of A, that is, tr(A) = 2i + b - 2, where b and i are the numbers of boundary and interior points of the convex hull [A] of A respectively. We conjecture the following discrete analog of the Brunn?Minkowski inequality: for any two finite point sets A, B c R2 one has tr(A + B) >= tr(A)1/2 + tr(B)1/2. We prove this conjecture in the cases where [A]=[B], B = A U {b}, |B| = 3 and if A and B have no interior points. A generalization to larger dimensions is also discussed.

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