A note on arrays of dots with distinct slopes

Abstract

We prove that the maximum number of dots in ann×n array of dots with distinct slopes is at leastcn 2/3(logn)−1/3 withc>0. This improves a previous result ofcn 1/2. An upper bound isO(n 4/5).

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References

  1. [1]

    Paul Erdős, Ron L. Graham, Imre Z. Ruzsa andHerbert Taylor: Bounds for Arrays of Dots with Distinct Slopes or Length,Combinatorica 12 (1992), 39–44.

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This research is supported in part by NSF under the grant NCR-8905052.

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Zhang, Z. A note on arrays of dots with distinct slopes. Combinatorica 13, 127–128 (1993). https://doi.org/10.1007/BF01202795

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