A note on Borsuk’s problem in Minkowski spaces

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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.

作者简介

A. Raigorodskii

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

编辑信件的主要联系方式.
Email: mraigor@yandex.ru
俄罗斯联邦, Moscow; Moscow; Maykop; Ulan-Ude

A. Sagdeev

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

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

参考

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