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- W4288621364 abstract "A difference basis with respect to $n$ is a subset $A subseteq mathbb{Z}$ such that $A - A supseteq {1, ldots, n}$. R'{e}dei and R'{e}nyi showed that the minimum size of a difference basis with respect to $n$ is $(c+o(1))sqrt{n}$ for some positive constant $c$. The best previously known lower bound on $c$ is $c geqslant 1.5602ldots$, which was obtained by Leech using a version of an earlier argument due to R'{e}dei and R'{e}nyi. In this note we use Fourier-analytic tools to show that the Leech--R'{e}dei--R'{e}nyi lower bound is not sharp." @default.
- W4288621364 created "2022-07-30" @default.
- W4288621364 creator A5019172041 @default.
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- W4288621364 date "2019-01-27" @default.
- W4288621364 modified "2023-09-29" @default.
- W4288621364 title "Improved Lower Bound for Difference Bases" @default.
- W4288621364 doi "https://doi.org/10.48550/arxiv.1901.09411" @default.
- W4288621364 hasPublicationYear "2019" @default.
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