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On the Simplest Inverse Problem for Sums of Sets in Several Dimensions

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d

-dimensional sets having the smallest cardinality of the sum set. Let be a finite d-dimensional set such that . If , then K consists of d parallel arithmetic progressions with the same common difference. We also establish the structure of K in the remaining cases .

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Authors and Affiliations

  1. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University; Ramat Aviv, Israel 69978; E-mail: ionut@math.tau.ac.il, , , , , , IL

    Yonutz Stanchescu

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  1. Yonutz Stanchescu
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Received: February 5, 1996/Revised: November 20, 1997

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Stanchescu, Y. On the Simplest Inverse Problem for Sums of Sets in Several Dimensions. Combinatorica 18, 139–149 (1998). https://doi.org/10.1007/PL00009808

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  • DOI: https://doi.org/10.1007/PL00009808

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