Sets without k‐term progressions can have many shorter progressions

DOI10.1002/rsa.20984zbMath1523.11018arXiv1908.09905OpenAlexW3112255858MaRDI QIDQ6049996

Cosmin Pohoata, Jacob Fox

Publication date: 11 October 2023

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.09905

zbMATH Keywords

arithmetic progressionsprobabilistic methodsadditive combinatoricsSzemerédi's theorem

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Arithmetic progressions (11B25) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (3)

The Elekes-Szabó problem and the uniformity conjecture ⋮ New lower bounds for van der Waerden numbers ⋮ Four‐term progression free sets with three‐term progressions in all large subsets

Cites Work

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• A new proof of Szemerédi's theorem for arithmetic progressions of length four
• New proofs of Plünnecke-type estimates for product sets in groups
• Dependent random choice
• On sets of integers containing k elements in arithmetic progression
• How Many 3-Term Arithmetic Progressions Can There Be If There Are No Longer Ones?
• NEW BOUNDS FOR SZEMERÉDI'S THEOREM, III: A POLYLOGARITHMIC BOUND FOR
• A new proof of Szemerédi's theorem

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