Sets Avoiding Six-Term Arithmetic Progressions in $\mathbb{Z}_6^{n}$ are Exponentially Small

DOI10.1137/21M1413766zbMath1495.11020arXiv2009.11897OpenAlexW3088787028MaRDI QIDQ5074952

Richárd Palincza, Péter Pál Pach

Publication date: 10 May 2022

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2009.11897

zbMATH Keywords

arithmetic progressionspolynomial methodsupersaturation

Mathematics Subject Classification ID

Arithmetic progressions (11B25) Extremal combinatorics (05D99)

Related Items (1)

Bounds on the size of progression-free sets in \(\mathbb{Z}_m^n\)

Cites Work

• Progression-free sets in \(\mathbb{Z}_4^n\) are exponentially small
• On large subsets of \(\mathbb{F}_q^n\) with no three-term arithmetic progression
• Extensions of generalized product caps
• A tight bound for Green's arithmetic triangle removal lemma in vector spaces
• Caps and progression-free sets in \(\mathbb{Z}_m^n\)
• Improved bounds for progression-free sets in \(C_8^n\)
• On cap sets and the group-theoretic approach to matrix multiplication
• On sets of integers which contain no three terms in geometric progression
• Four‐term progression free sets with three‐term progressions in all large subsets

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