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Creators/Authors contains: "Manners, Freddie"

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  1. ; ; (, Random Structures & Algorithms)
    Abstract The entropic doubling of a random variable taking values in an abelian group is a variant of the notion of the doubling constant of a finite subset of , but it enjoys somewhat better properties; for instance, it contracts upon applying a homomorphism. In this paper we develop further the theory of entropic doubling and give various applications, including: (1) A new proof of a result of Pálvölgyi and Zhelezov on the “skew dimension” of subsets of with small doubling; (2) A new proof, and an improvement, of a result of the second author on the dimension of subsets of with small doubling; (3) A proof that the Polynomial Freiman–Ruzsa conjecture over implies the (weak) Polynomial Freiman–Ruzsa conjecture over . 
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    Free, publicly-accessible full text available July 31, 2025
  2. ; ; (, Proceedings of the London Mathematical Society)
    Abstract A transversal in an latin square is a collection of entries not repeating any row, column, or symbol. Kwan showed that almost every latin square has transversals as . Using a loose variant of the circle method we sharpen this to . Our method works for all latin squares satisfying a certain quasirandomness condition, which includes both random latin squares with high probability as well as multiplication tables of quasirandom groups. 
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  3. ; ; (, Journal of Combinatorial Theory, Series B)
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