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Exponentially Ramsey Sets

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Abstract

We study chromatic numbers of spaces \(\mathbb{R}_p^n=(\mathbb{R}^n, \ell_p)\) with forbidden monochromatic sets. For some sets, we for the first time obtain explicit exponentially growing lower bounds for the corresponding chromatic numbers; for some others, we substantially improve previously known bounds.

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Authors and Affiliations

  1. Laboratory of Advanced Combinatorics and Network Applications, Moscow Institute of Physics and Technology (State University), Moscow, Russia

    A. A. Sagdeev

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Original Russian Text © A.A. Sagdeev, 2018, published in Problemy Peredachi Informatsii, 2018, Vol. 54, No. 4, pp. 82–109.

Supported in part by the Russian Foundation for Basic Research, project no. 18-01-00355, and the President of the Russian Federation Council for State Support of Leading Scientific Schools, grant no. NSh-6760.2018.1.

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Sagdeev, A.A. Exponentially Ramsey Sets. Probl Inf Transm 54, 372–396 (2018). https://doi.org/10.1134/S0032946018040051

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  • DOI: https://doi.org/10.1134/S0032946018040051

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