On the chromatic number of slices without monochromatic unit arithmetic progressions
https://doi.org/10.22405/2226-8383-2023-24-4-78-84
Abstract
For ℎ, 𝑛 ≥ 1 and 𝑒 > 0 we consider a chromatic number of the spaces R^𝑛×[0, 𝑒]^ℎ and general results in this problem. Also we consider the chromatic number of normed spaces with forbidden monochromatic arithmetic progressions. We show that for any 𝑛 there exists a two-coloring of R^𝑛 such that all long unit arithmetic progressions contain points of both colors and this coloring covers spaces of the form R^𝑛×[0,𝑒]^ℎ.
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Review
For citations:
Kirova V.O. On the chromatic number of slices without monochromatic unit arithmetic progressions. Chebyshevskii Sbornik. 2023;24(4):78-84. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-4-78-84
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