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- W2914590968 abstract "A difference basis with respect to $n$ is a subset $A subseteq mathbb{Z}$ such that $A - A supseteq {1, ldots, n}$. Redei and Renyi 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 Redei and Renyi. In this note we use Fourier-analytic tools to show that the Leech--Redei--Renyi lower bound is not sharp." @default.
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- W2914590968 date "2019-01-27" @default.
- W2914590968 modified "2023-09-27" @default.
- W2914590968 title "Improved Lower Bound for Difference Bases" @default.
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