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Borsuk’s partition conjecture

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Japanese Journal of Mathematics Aims and scope

Abstract

In 1933, Borsuk proposed the following problem: Can every bounded set in \({{\mathbb{E}}^n}\) be divided into n + 1 subsets of smaller diameter? This problem has been studied by many authors, and a lot of partial results have been discovered. In particular, Kahn and Kalai’s counterexamples surprised the mathematical community in 1993. Nevertheless, the problem is still far away from being completely resolved. This paper presents a broad review on related subjects and, based on a novel reformulation, introduces a computer proof program to deal with this challenging problem.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (NSFC11921001), the National Key Research and Development Program of China (2018YFA0704701), and 973 Program 2013CB834201. The author is grateful to the referee for his helpful suggestions.

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Authors and Affiliations

  1. Center for Applied Mathematics, Tianjin University, Tianjin, China

    Chuanming Zong

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  1. Chuanming Zong
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Correspondence to Chuanming Zong.

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Communicated by: Toshiyuki Kobayashi

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Zong, C. Borsuk’s partition conjecture. Jpn. J. Math. 16, 185–201 (2021). https://doi.org/10.1007/s11537-021-2007-7

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  • DOI: https://doi.org/10.1007/s11537-021-2007-7

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