Borsuk Conjecture - four

References

• Wikipedia

• [Bo33] Borsuk, K. (1933). Drei Sätze über die n-dimensionale euklidische Sphäre. Fundamenta Mathematicae 20, 177–190. https://doi.org/10.4064/fm-20-1-177-190
• [Pe47] Perkal, J. (1947). Sur la subdivision des ensembles en parties de diamètre inférieur. Colloquium Mathematicum 2, 45.
• [Eg55] Eggleston, H. G. (1955). Covering a three-dimensional set with sets of smaller diameter. Journal of the London Mathematical Society 30, 11–24. https://doi.org/10.1112/jlms/s1-30.1.11
• [La82] Lassak, M. (1982). An estimate concerning Borsuk partition problem. Bulletin of the Polish Academy of Sciences, Mathematics 30(9–10), 449–451.
• [KK93] Kahn, J., Kalai, G. (1993). A counterexample to Borsuk's conjecture. Bulletin of the American Mathematical Society 29(1), 60–62. https://arxiv.org/abs/math/9307229
• [Bo14] Bondarenko, A. (2014). On Borsuk's conjecture for two-distance sets. Discrete & Computational Geometry 51(3), 509–515. https://doi.org/10.1007/s00454-014-9579-4
• [JB14] Jenrich, T., Brouwer, A. E. (2014). A 64-dimensional counterexample to Borsuk's conjecture. Electronic Journal of Combinatorics 21(4), P4.29. https://doi.org/10.37236/4069
• [Gr26] Grinsztajn, M. (2026). A 63-dimensional counterexample to Borsuk's conjecture. Proof note and verification script, https://github.com/maaxgrin/borsuk-63-counterexample
• [Ji26] Ji, Y. (2026). An AI generated counterexample to Borsuk problem in dimension 63. https://arxiv.org/abs/2608.12561 (withdrawn as a duplicate of [Gr26])
• [TV26] Tolmachev, A., Voronov, V. (2026). *Reducing the upper bound for the Borsuk number in $\mathbb{R}^4$ to 8*. https://arxiv.org/abs/2605.19068
• [OP28a] Tao, T. et al., Optimization problems, constant 28a (smallest Borsuk counterexample dimension). https://teorth.github.io/optimizationproblems/constants/28a.html
• [Ka15] Kalai, G. (2015). Some old and new problems in combinatorial geometry I: Around Borsuk's problem. https://arxiv.org/abs/1505.04952