A Note on Borsuk’s Problem in Minkowski Spaces

In 1993, Kahn and Kalai famously constructed a sequence of finite sets in d -dimensional Euclidean spaces that cannot be partitioned into less than parts of smaller diameter. Their method works not only for the Euclidean, but for all -spaces as well. In this short note, we observe that the larger th...

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Bibliographic Details
Published in:Doklady. Mathematics 2024-02, Vol.109 (1), p.80-83
Main Authors: Raigorodskii, A. M., Sagdeev, A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Minkowski space
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Summary:In 1993, Kahn and Kalai famously constructed a sequence of finite sets in d -dimensional Euclidean spaces that cannot be partitioned into less than parts of smaller diameter. Their method works not only for the Euclidean, but for all -spaces as well. In this short note, we observe that the larger the value of p , the stronger this construction becomes.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562424701849