A lattice point problem and additive number theory | Zendy

Noga Alon | Zendy; Moshe Dubiner | Zendy

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A lattice point problem and additive number theory

Author(s) -

Noga Alon,

Moshe Dubiner

Publication year - 1995

Publication title -

combinatorica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.106

H-Index - 58

eISSN - 1439-6912

pISSN - 0209-9683

DOI - 10.1007/bf01299737

Subject(s) - mathematics , combinatorics , lattice (music) , euclidean geometry , euclidean space , cardinality (data modeling) , eigenvalues and eigenvectors , discrete mathematics , geometry , physics , quantum mechanics , computer science , acoustics , data mining

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 car- dinality 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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