A lattice point problem and additive number theory

Noga Alon, Moshe Dubiner

Research output: Contribution to journalArticlepeer-review

58 Scopus citations


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 languageEnglish (US)
Pages (from-to)301-309
Number of pages9
Issue number3
StatePublished - Sep 1995
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics


  • Mathematics Subject Classification (1991): 11B75


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