English

Discrete Kakeya-type problems and small bases

Combinatorics 2008-04-06 v2 Group Theory Number Theory

Abstract

A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and use them to resolve an old question of Erdos and Newman on bases for sets of integers, and to obtain several extensions for other groups.

Keywords

Cite

@article{arxiv.0711.1604,
  title  = {Discrete Kakeya-type problems and small bases},
  author = {Noga Alon and Boris Bukh and Benny Sudakov},
  journal= {arXiv preprint arXiv:0711.1604},
  year   = {2008}
}

Comments

12 pages

R2 v1 2026-06-21T09:42:10.266Z