A Lattice Point Problem and Additive Number Theory

نویسندگان

  • Noga Alon
  • Moshe Dubiner
چکیده

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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عنوان ژورنال:
  • Combinatorica

دوره 15  شماره 

صفحات  -

تاریخ انتشار 1995