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How often can a given distance occur in a finite set of integers?

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Abstract.

Let n, a, d be natural numbers and A a set of integers of the closed interval [0, n] with | A | = a. Then we establish sharp lower and upper bounds for the number of pairs \((x,y)\in A\times A\) for which y–x = d. Roughly spoken, we investigate how often a distance d can occur in A.

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  1. Mathematisches Institut der Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany, , , , , , DE

    Egbert Harzheim

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  1. Egbert Harzheim
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Received: 16.7.1997

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Harzheim, E. How often can a given distance occur in a finite set of integers?. Arch. Math. 73, 114–118 (1999). https://doi.org/10.1007/s000130050375

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  • DOI: https://doi.org/10.1007/s000130050375

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