Economical coverings of sets of lattice points

N. Alon

doi:10.1007/BF01896202

Economical coverings of sets of lattice points

N. Alon^*

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let t(n, d) be the minimum number t such that there are t of the n^d lattice points {Mathematical expression} so that the (₂^t) lines that they determine cover all the above n^d lattice points. We prove that for every integer d≥2 there are two positive constants c₁=c₁(d) and c₂=c₂(d) such that for every n {Mathematical expression} The special case d=2 settles a problem of Erdös and Purdy.

Original language	English
Pages (from-to)	225-230
Number of pages	6
Journal	Geometric and Functional Analysis
Volume	1
Issue number	3
DOIs	https://doi.org/10.1007/BF01896202
State	Published - Sep 1991

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abstract = "Let t(n, d) be the minimum number t such that there are t of the nd lattice points {Mathematical expression} so that the (2t) lines that they determine cover all the above nd lattice points. We prove that for every integer d≥2 there are two positive constants c1=c1(d) and c2=c2(d) such that for every n {Mathematical expression} The special case d=2 settles a problem of Erd{\"o}s and Purdy.",

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AB - Let t(n, d) be the minimum number t such that there are t of the nd lattice points {Mathematical expression} so that the (2t) lines that they determine cover all the above nd lattice points. We prove that for every integer d≥2 there are two positive constants c1=c1(d) and c2=c2(d) such that for every n {Mathematical expression} The special case d=2 settles a problem of Erdös and Purdy.

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Economical coverings of sets of lattice points

Abstract

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