Improved lower bound for difference bases

[摘要] A difference basis with respect to n is a subset A subset of Z such that A - A superset of {1, . . , n}. Redei and Renyi showed that the minimum size of a difference basis with respect to n is (c + o(1))root n for some positive constant c. The best previously known lower bound on c is c >= 1.5602..., which was obtained by Leech using a version of an earlier argument due to Redei and Renyi. In this note we use Fourier-analytic tools to show that the Leech Redei Renyi lower bound is not sharp. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Difference basis;Fourier analysis