### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 301-309 |

Number of pages | 9 |

Journal | Combinatorica |

Volume | 15 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 1995 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Computational Mathematics

### Keywords

- Mathematics Subject Classification (1991): 11B75

## Fingerprint Dive into the research topics of 'A lattice point problem and additive number theory'. Together they form a unique fingerprint.

## Cite this

Alon, N., & Dubiner, M. (1995). A lattice point problem and additive number theory.

*Combinatorica*,*15*(3), 301-309. https://doi.org/10.1007/BF01299737