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Creators/Authors contains: "Xu, Max Wenqiang"

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  1. ; (, Journal d'Analyse Mathématique)
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  2. ; ; (, Compositio Mathematica)
    Celebrated theorems of Roth and of Matoušek and Spencer together show that the discrepancy of arithmetic progressions in the first $$n$$ positive integers is $$\Theta (n^{1/4})$$ . We study the analogous problem in the $$\mathbb {Z}_n$$ setting. We asymptotically determine the logarithm of the discrepancy of arithmetic progressions in $$\mathbb {Z}_n$$ for all positive integer $$n$$ . We further determine up to a constant factor the discrepancy of arithmetic progressions in $$\mathbb {Z}_n$$ for many $$n$$ . For example, if $n=p^k$ is a prime power, then the discrepancy of arithmetic progressions in $$\mathbb {Z}_n$$ is $$\Theta (n^{1/3+r_k/(6k)})$$ , where $$r_k \in \{0,1,2\}$$ is the remainder when $$k$$ is divided by $$3$$ . This solves a problem of Hebbinghaus and Srivastav. 
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  3. ; ; ; (, Journal of Graph Theory)
    Abstract The list Ramsey number , recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list‐coloring variant of the classical Ramsey number. They showed that if is a fixed ‐uniform hypergraph that is not ‐partite and the number of colors goes to infinity, . We prove that if and only if is not ‐partite. 
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