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.
Keywords:chromatic number of spheres, linear-algebraic method, Frankl–Wilson theorem, Nelson–Hadwiger problem, distance graphs.
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