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arXiv · 1307.6316

On sumsets and convex hull

Karoly Boroczky·Francisco Santos·Oriol Serra
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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.

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Karoly Boroczky, Francisco Santos, Oriol Serra. 2013-07-24. On sumsets and convex hull. https://doi.org/10.1007/s00454-014-9633-2

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