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On the Correlation Measures of Subsets

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Abstract

In a series of papers, Dartyge and Sárközy (partly with other coauthors) studied pseudorandom subsets. In this paper, we study the minimal values of correlation measures of pseudorandom subsets by extending the methods introduced in Alon et al. (Comb Probab Comput 15:1–29, 2006), Anantharam (Discrete Math 308:6203–6209, 2008), Gyarmati (Stud Sci Math Hung 42:79–93, 2005) and Gyarmati and Mauduit (Discrete Math 312:811–818, 2012).

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Notes

  1. If \((u_n)_{n\in {\mathbb {N}}}\) and \((v_n)_{n\in {\mathbb {N}}}\) are two sequences of positive real numbers, the notation \( u_n \ll v_n\) means that there exists a positive constant c such that, for any \(n \in {\mathbb {N}}\), we have \( u_n \le c v_n\).

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Acknowledgements

Parts of this paper were written during a pleasant visit of Huaning Liu to Marseille. He wishes to thank the Institut de Mathématiques de Marseille for kind hospitality and support. This work is supported by National Natural Science Foundation of China under Grant no. 11571277, and the Science and Technology Program of Shaanxi Province of China under Grant no. 2014KJXX-61, 2016GY-080 and 2016GY-077.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, Shaanxi, People’s Republic of China

    Huaning Liu

  2. Institut de Mathématiques de Marseille, UMR 7373 CNRS, Aix-Marseille University and Institut Universitaire de France, 163 Avenue de Luminy, Case 907, 13288, Marseille, Cedex 9, France

    Christian Mauduit

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Liu, H., Mauduit, C. On the Correlation Measures of Subsets. Ann. Comb. 24, 311–336 (2020). https://doi.org/10.1007/s00026-019-00488-x

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