Borsuk's Conjecture Fails in Dimensions 321 and 322

2002/02/12 by Oleg Pikhurko, Pikhurko, Oleg
Engineering · Mathematics · #52Cxx #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems #math.CO #msc:52Cxx

paper · pdf · doi:10.48550/arxiv.math/0202112

3 pages

arxiv created 2002/02/12 · openalex publication_date 2002/02/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Borsuk's conjecture states that any bounded set in Rⁿ can be partitioned into n+1 sets of smaller diameter. It is known to be false for all n bigger or equal to 323. Here we show that Borsuk's conjecture fails in dimensions 321 and 322. (This result has been independently discovered by Hinrichs and Richter.)

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