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Progression-free sets in $$\mathbb{Z}_4^n$$ are exponentially small. (English) Zbl 1425.11019
Summary: We show that for an integer $$n\geq 1$$, any subset $$A\subseteq\mathbb{Z}_4^n$$ free of three-term arithmetic progressions has size $$|A|\leq 4^{\gamma n}$$, with an absolute constant $$\gamma\approx 0.926$$.

##### MSC:
 11B30 Arithmetic combinatorics; higher degree uniformity 11B25 Arithmetic progressions 51E20 Combinatorial structures in finite projective spaces
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