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arXiv · 1610.00247

The large $k$-term progression-free sets in $\mathbb{Z}_q^n$

Hongze Li
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Abstract

Let $k$ and $n$ be fixed positive integers. For each prime power $q\geqslant k\geqslant 3$, we show that any subset $A\subseteq \mathbb{Z}_q^n$ free of $k$-term arithmetic progressions has size $|A|\leqslant c_k(q)^n$ with a constant $c_k(q)$ that can be expressed explicitly in terms of $k$ and $q$. As a consequence, we can take $c_k(q)=0.8415q$ for sufficiently large $q$ and arbitrarily fixed $k\geq 3$.

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Hongze Li. 2016-10-02. The large $k$-term progression-free sets in $\mathbb{Z}_q^n$. https://arxiv.org/abs/1610.00247

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