Discrete Kakeya-type problems and small bases

Noga Alon; Boris Bukh; Benny Sudakov

doi:10.1007/s11856-009-0115-9

Discrete Kakeya-type problems and small bases

Noga Alon, Boris Bukh, Benny Sudakov

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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

Original language	English
Pages (from-to)	285-301
Number of pages	17
Journal	Israel Journal of Mathematics
Volume	174
Issue number	1
DOIs	https://doi.org/10.1007/s11856-009-0115-9
State	Published - 1 Nov 2009
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-009-0115-9

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title = "Discrete Kakeya-type problems and small bases",

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 Erd{\'o}s and Newman on bases for sets of integers, and to obtain several extensions for other groups.",

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AU - Bukh, Boris

AU - Sudakov, Benny

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/74249105263

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DO - 10.1007/s11856-009-0115-9

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JO - Israel Journal of Mathematics

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IS - 1

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Discrete Kakeya-type problems and small bases

Abstract

ASJC Scopus subject areas

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