Discrete Kakeya-type problems and small bases

Noga Alon*, Boris Bukh, Benny Sudakov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 Erdós and Newman on bases for sets of integers, and to obtain several extensions for other groups.

Original languageEnglish
Pages (from-to)285-301
Number of pages17
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Nov 2009


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