Functiones et Approximatio Commentarii Mathematici

On sum-free subsets of the torus group

Vsevolod F. Lev

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Establishing the structure of dense sum-free subsets of the torus group $\mathbb{R}/\mathbb{Z}$, we find an absolute constant $\alpha_0<1/3$ such that for any sum-free subset $A\subseteq\mathbb{R}/\mathbb{Z}$ with the inner measure $\mu(A)>\alpha_0$ there exists an integer $q\ge 1$ so that $$A \subseteq \bigcup_{j=0}^{q-1}[ \frac{j+\mu(A)}q, \frac{j+1-\mu(A)}q ].$$

Article information

Funct. Approx. Comment. Math., Volume 37, Number 2 (2007), 277-283.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P70: Inverse problems of additive number theory, including sumsets
Secondary: 11B75: Other combinatorial number theory

sum-free sets


Lev, Vsevolod F. On sum-free subsets of the torus group. Funct. Approx. Comment. Math. 37 (2007), no. 2, 277--283. doi:10.7169/facm/1229619653.

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