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

Mathematics

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 (US)
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 - Nov 2009

All Science Journal Classification (ASJC) codes

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.",

author = "Noga Alon and Boris Bukh and Benny Sudakov",

note = "Funding Information: ∗Research supported in part by a USA Israeli BSF grant, by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, by an ERC ad-vanced grant, by NSF grant CCF 0832797 and by the Ambrose Monell Foundation. ∗∗Research supported in part by NSF CAREER award DMS-0812005, NSF grant DMS-0635607, by a USA-Israeli BSF grant, and by the State of New Jersey. Received November 10, 2007 and in revised form March 31, 2008",

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T1 - Discrete Kakeya-type problems and small bases

AU - Alon, Noga

AU - Bukh, Boris

AU - Sudakov, Benny

N1 - Funding Information: ∗Research supported in part by a USA Israeli BSF grant, by the Hermann Minkowski Minerva Center for Geometry at Tel Aviv University, by an ERC ad-vanced grant, by NSF grant CCF 0832797 and by the Ambrose Monell Foundation. ∗∗Research supported in part by NSF CAREER award DMS-0812005, NSF grant DMS-0635607, by a USA-Israeli BSF grant, and by the State of New Jersey. Received November 10, 2007 and in revised form March 31, 2008

PY - 2009/11

Y1 - 2009/11

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

UR - https://www.scopus.com/pages/publications/74249105263#tab=citedBy

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DO - 10.1007/s11856-009-0115-9

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SP - 285

EP - 301

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1

ER -

Discrete Kakeya-type problems and small bases

Abstract

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