## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  774.05020
Autor:  Erdös, Paul; Graham, Ron; Ruzsa, Imre Z.; Taylor, Herbert
Title:  Bounds for arrays of dots with distinct slopes or lengths. (In English)
Source:  Combinatorica 12, No.1, 39-44 (1992).
Review:  Authors' abstract: An n× m sonar sequence is a subset of the n× m grid with exactly one point in each column, such that the {m\choose 2} vectors determined by them are all distinct. We show that for fixed n the maximal m for which a sonar sequence exists satisfies n-Cn11/20 < m < n+4n2/3 for all the n and m > n+c log n log log n for infinitely many n.
Another problem concerns the maximal number D of points that can be selected from the n× m grid so that all the \binom{D}{2} vectors have slopes. We prove n ½ << D << n4/5.
Reviewer:  J.R.Seberry (Lincoln)
Classif.:  * 05B15 Orthogonal arrays, etc.
05B30 Other designs, configurations
Keywords:  arrays of dots; sonar sequence; slopes

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