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

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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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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  • AMS Subject Classification (1991) Classes:  11B13, 11P99, 52C99