Hilbert cubes in progression-free sets and in the set of squares II

Christian Elsholtz; Rainer Dietmann

arxiv: 1207.1461 · v1 · pith:TTFTVZF2new · submitted 2012-07-05 · 🧮 math.NT · math.CO

Hilbert cubes in progression-free sets and in the set of squares II

Rainer Dietmann , Christian Elsholtz This is my paper

classification 🧮 math.NT math.CO

keywords hilbertsquaresboundedcubecubesdimensionintegerprogression-free

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Let $S_2$ be the set of integer squares. We show that the dimension $d$ of a Hilbert cube $a_0+\{0,a_1\}+...+ \{0, a_d\}\subset S_2$ is bounded by $d=O(\log \log N)$

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Hilbert cubes in progression-free sets and in the set of squares II

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