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Combinatorica

, Volume 15, Issue 3, pp 301–309 | Cite as

A lattice point problem and additive number theory

  • Noga Alon
  • Moshe Dubiner
Article

Abstract

For every dimensiond≥1 there exists a constantc=c(d) such that for alln≥1, every set of at leastcn lattice points in thed-dimensional Euclidean space contains a subset of cardinality preciselyn 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.

Mathematics Subject Classification (1991)

11 B 75 

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Noga Alon
    • 1
  • Moshe Dubiner
    • 1
  1. 1.Department of Mathematics Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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