An Upper Bound for d-dimensional Difference Sets

Let be the maximal positive number for which the inequality holds for every finite set of affine dimension . What can one say about ? The exact value of is known only for d = 1, 2 and 3. It is shown that , for every . This disproves a conjecture of Ruzsa. Some further related questions are posed and discussed.

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Received March 27, 2000

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V. Stanchescu, Y. An Upper Bound for d-dimensional Difference Sets. Combinatorica 21, 591–595 (2001).

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  • AMS Subject Classification (2000) Classes:  52C10, 05D05, 11P70, 11B75