Open Problem Garden

Retkes, Zoltan

Inequality for square summable complex series ★★

Author(s): Retkes

Conjecture For all $\alpha=(\alpha_1,\alpha_2,\ldots)\in l_2(\cal{C})$ the following inequality holds $\sum_{n\geq 1}|\alpha_n|^2\geq \frac{6}{\pi^2}\sum_{k\geq0}\bigg| \sum_{l\geq0}\frac{1}{l+1}\alpha_{2^k(2l+1)}\bigg|^2$

Keywords: Inequality

Posted by tigris35711
updated October 29th, 2014

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Logic » Finite Model Theory

Vertex Cover Integrality Gap ★★

Author(s): Atserias

Conjecture For every $\varepsilon > 0$ there is $\delta > 0$ such that, for every large $n$ , there are $n$ -vertex graphs $G$ and $H$ such that $G \equiv_{\delta n}^{\mathrm{C}} H$ and $\mathrm{vc}(G) \ge (2 - \varepsilon) \cdot \mathrm{vc}(H)$ .