An example concerning set addition in F_2^n
| Autor: | Green, BJ, Kane, D |
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| Rok vydání: | 2017 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1703.01036 |
| Popis: | We construct sets $A, B$ in a vector space over $\mathbb{F}_2$ with the property that $A$ is "statistically" almost closed under addition by $B$ in the sense that $a + b$ almost always lies in $A$ when $a \in A, b \in B$, but which is extremely far from being "combinatorially" almost closed under addition by $B$: if $A' \subset A$, $B' \subset B$ and $A' + B'$ is comparable in size to $A'$ then $|B'| \lessapprox |B|^{1/2}$. Comment: 5 pages, to appear in "Harmonic analysis, approximation theory and number theory", special volume of Proc Steklov Math. Inst. in honour of the 60th birthday of Sergei Konyagin |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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