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- W1549301089 abstract "ErdH{o}s conjectured that for any set $Asubseteq mathbb{N}$ with positive lower asymptotic density, there are infinite sets $B,Csubseteq mathbb{N}$ such that $B+Csubseteq A$. We verify ErdH{o}s' conjecture in the case that $A$ has Banach density exceeding $frac{1}{2}$. As a consequence, we prove that, for $Asubseteq mathbb{N}$ with positive Banach density (a much weaker assumption than positive lower density), we can find infinite $B,Csubseteq mathbb{N}$ such that $B+C$ is contained in the union of $A$ and a translate of $A$. Both of the aforementioned results are generalized to arbitrary countable amenable groups. We also provide a positive solution to ErdH{o}s' conjecture for subsets of the natural numbers that are pseudorandom." @default.
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- W1549301089 date "2015-08-01" @default.
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- W1549301089 title "On a Sumset Conjecture of Erdős" @default.
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- W1549301089 doi "https://doi.org/10.4153/cjm-2014-016-0" @default.
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