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On Lower Bounds for the Chromatic Number of Spheres

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Abstract

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.

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  1. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, 141701, Russia

    O. A. Kostina

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  1. O. A. Kostina
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Russian Text © O. A. Kostina, 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 1, pp. 18–31.

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Kostina, O.A. On Lower Bounds for the Chromatic Number of Spheres. Math Notes 105, 16–27 (2019). https://doi.org/10.1134/S0001434619010036

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