Economical coverings of sets of lattice points

N. Alon

doi:10.1007/BF01896202

Economical coverings of sets of lattice points

N. Alon

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 (US)
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
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/BF01896202

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title = "Economical coverings of sets of lattice points",

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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year = "1991",

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AU - Alon, N.

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N2 - 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.

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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UR - https://www.scopus.com/pages/publications/34249923697#tab=citedBy

U2 - 10.1007/BF01896202

DO - 10.1007/BF01896202

M3 - Article

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SN - 1016-443X

VL - 1

SP - 225

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Economical coverings of sets of lattice points

Abstract

All Science Journal Classification (ASJC) codes

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