Ackermann-type bounds are unavoidable for the hypergraph regularity lemma for every k ≥ 2.
Szemer´ edi, On sets of integers containing no k elements in arithmetic progression, Acta Arith
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A Tight Bound for Hyperaph Regularity
Ackermann-type bounds are unavoidable for the hypergraph regularity lemma for every k ≥ 2.