On Lower Bounds for the Chromatic Number of Spheres

Estimates of the chromatic numbers of spheres are studied. The optimality of the choice of the parameters of the linear-algebraic method used to obtain these estimates is investigated. For the case of (0, 1)-vectors, it is shown that the parameters chosen in previous results yield the best estimate....

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Bibliographic Details
Published in:Mathematical Notes 2019, Vol.105 (1-2), p.16-27
Main Author: Kostina, O. A.
Format: Article
Language:English
Subjects:
Estimates
Lower bounds
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization
Parameters
Vectors (mathematics)
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Summary:Estimates of the chromatic numbers of spheres are studied. The optimality of the choice of the parameters of the linear-algebraic method used to obtain these estimates is investigated. For the case of (0, 1)-vectors, it is shown that the parameters chosen in previous results yield the best estimate. For the case of (−1, 0, 1)-vectors, the optimal values of the parameters are obtained; this leads to a significant refinement of the estimates of the chromatic numbers of spheres obtained earlier.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434619010036