A Lattice Point Problem and Additive Number Theory
نویسندگان
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