A lattice point problem and additive number theory

Noga Alon; Moshe Dubiner

doi:10.1007/BF01299737

A lattice point problem and additive number theory

Noga Alon
, Moshe Dubiner

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

64 Scopus citations

Abstract

For every dimension d≥1 there exists a constant c=c(d) such that for all n≥1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues.

Original language	English (US)
Pages (from-to)	301-309
Number of pages	9
Journal	Combinatorica
Volume	15
Issue number	3
DOIs	https://doi.org/10.1007/BF01299737
State	Published - Sep 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

Keywords

Mathematics Subject Classification (1991): 11B75

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10.1007/BF01299737

Cite this

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title = "A lattice point problem and additive number theory",

abstract = "For every dimension d≥1 there exists a constant c=c(d) such that for all n≥1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues.",

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AU - Dubiner, Moshe

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N2 - For every dimension d≥1 there exists a constant c=c(d) such that for all n≥1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues.

AB - For every dimension d≥1 there exists a constant c=c(d) such that for all n≥1, every set of at least cn lattice points in the d-dimensional Euclidean space contains a subset of cardinality precisely n whose centroid is also a lattice point. The proof combines techniques from additive number theory with results about the expansion properties of Cayley graphs with given eigenvalues.

KW - Mathematics Subject Classification (1991): 11B75

UR - https://www.scopus.com/pages/publications/0001496856

UR - https://www.scopus.com/pages/publications/0001496856#tab=citedBy

U2 - 10.1007/BF01299737

DO - 10.1007/BF01299737

M3 - Article

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VL - 15

SP - 301

EP - 309

JO - Combinatorica

JF - Combinatorica

IS - 3

ER -

A lattice point problem and additive number theory

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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