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G. Wegner [12] gave a geometric characterization of all so–called Groe-mer packing of n ≥ 2 unit discs in E 2 that are densest packings of n unit discs with respect to the convex hull of the discs. In this paper we provide a number theoretic characterization of all n satisfying that such a " Wegner packing " of n unit discs exists, and show that the… (More)

One classical result of Freiman gives the optimal lower bound for the cardinality of A + A if A is a d-dimensional finite set in R d. 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… (More)

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