Discrete Kakeya-type problems and small bases |
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| Authors: | Noga Alon Boris Bukh Benny Sudakov |
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| Institution: | 1.Schools of Mathematics and Computer Science, Raymond and Beverly Sackler, Faculty of Exact Sciences,Tel Aviv University,Tel Aviv,Israel;2.Institute for Advanced Study,Princeton University,Princeton,USA;3.Center for Mathematical Sciences Cambridge,Cambridge,England;4.Churchill College Cambridge,Cambridge,England;5.Department of Mathematics,UCLA,Los Angeles,USA;6.Institute for Advanced Study,Princeton University,Princeton,USA |
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| 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 Erdős and Newman on bases for sets of integers, and to obtain
several extensions for other groups. |
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