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.
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