A note on Borsuk’s problem in Minkowski spaces

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Abstract

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 lp-spaces as well. In this short note, we observe that the larger the value of p, the stronger this construction becomes.

About the authors

A. M. Raigorodskii

Moscow Institute of Physics and Technology; Moscow State University; Caucasus Mathematical Center, Adyghe State University; Buryat State University

Author for correspondence.
Email: mraigor@yandex.ru
Russian Federation, Moscow; Moscow; Maykop; Ulan-Ude

A. Sagdeev

Alfred Renyi Institute of Mathematics; Moscow Institute of Physics and Technology

Email: sagdeevarsenii@gmail.com
Hungary, Budapest; Moscow, Russia

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