TY - JOUR
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 - http://www.scopus.com/inward/record.url?scp=74249105263&partnerID=8YFLogxK
U2 - 10.1007/s11856-009-0115-9
DO - 10.1007/s11856-009-0115-9
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AN - SCOPUS:74249105263
SN - 0021-2172
VL - 174
SP - 285
EP - 301
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -