Effective Bounds for Restricted $3$-Arithmetic Progressions in $\mathbb{F}_p^n$ by Amey Bhangale, Subhash Khot, Dor Minzer

“…It has been generalized and modified in multiple directions. Famously, Szemerédi proved the corresponding result for progressions of arbitrary length in 1975. …”
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An efficient asymmetric removal lemma and its limitations by Lior Gishboliner, Asaf Shapira, Yuval Wigderson

“…To this end, he devised a new variant of Szemerédi’s regularity lemma. We obtain the following results: • We first give a regularity-free proof of Csaba’s theorem, which improves the number of copies of $C_5$ to the optimal number $\operatorname {\mathrm {poly}}(\varepsilon )\cdot n^5$ …”
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