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On Dividing Sets into Parts of Smaller Diameter

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Abstract

An important generalization of Borsuk’s classical problem of partitioning sets into parts of smaller diameter is studied. New upper and lower bounds for the Borsuk numbers are found.

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REFERENCES

  1. A. M. Raigorodskii, “Cliques and cycles in distance graphs and graphs of diameters,” in Discrete Geometry and Algebraic Combinatorics, AMS Contemporary Mathematics, Vol. 625 (Am. Math. Soc., Providence, 2014), pp. 93–109.

  2. L. I. Bogolyubsky and A. M. Raigorodskii, Math. Notes 105 (1–2), 180–203 (2019).

    Article  MathSciNet  Google Scholar 

  3. V. P. Filimonov, Sb. Math. 205 (8), 1160–1200 (2014).

    Article  MathSciNet  Google Scholar 

  4. C. A. Rogers, Mathematika 10, 157–164 (1963).

    Article  MathSciNet  Google Scholar 

  5. J. Bourgain and J. Lindenstrauss, “On covering a set in by balls of the same diameter,” Geometric Aspects of Functional Analysis, Ed. by J. Lindenstrauss and V. Milman, Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1991), Vol. 1469, pp. 138–144.

  6. R. Ahlswede and L. H. Khachatrian, Eur. J. Comb. 18, 125–136 (1997).

    Article  Google Scholar 

  7. A. M. Raigorodskii and A. A. Kharlamova, “On collections of (–1, 0, 1)-vectors with constraints on the values of pairwise inner products,” Studies in Vector and Tensor Analysis (Mosk. Gos. Univ., Moscow, 2013), Vol. 29, pp. 130–146 [in Russian].

    Google Scholar 

  8. P. Frankl and A. Kupavskii, J. Comb. Theory Ser. A 155, 157–179 (2018).

    Article  Google Scholar 

  9. P. Frankl and A. Kupavskii, Combinatorica 39 (6), 1255–1266 (2019).

    Article  MathSciNet  Google Scholar 

  10. A. Kupavskii, J. Comb. Theory Ser. A 168, 272–287 (2019).

    Article  MathSciNet  Google Scholar 

  11. A. B. Kupavskii and A. A. Sagdeev, Russ. Math. Surv. 75 (5), 965–967 (2020).

  12. A. V. Bobu, A. E. Kupriyanov, and A. M. Raigorodskii, Math. Notes 107 (3), 392–403 (2020).

    Article  Google Scholar 

  13. A. M. Raigorodskii and A. A. Sagdeev, Acta Math. Univ. Comenianae 88 (3), 1029–1033 (2019).

    MathSciNet  Google Scholar 

  14. A. M. Raigorodskii and E. D. Shishunov, Dokl. Math. 99 (2), 165–166 (2019).

    Article  Google Scholar 

  15. F. A. Pushnyakov and A. M. Raigorodskii, Math. Notes 107 (2), 322–332 (2020).

    Article  Google Scholar 

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Funding

This work was supported by the Russian Foundation for Basic Research (project no. 18-01-00355) and by President’s grant NSh-2540.2020.1.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudnyi, Moscow oblast, Russia

    A. M. Raigorodskii

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119991, Moscow, Russia

    A. M. Raigorodskii

  3. Caucasus Mathematical Center, Adyghe State University, 385000, Maykop, Republic of Adygea, Russia

    A. M. Raigorodskii

  4. Institute of Mathematics and Computer Science, Buryat State University, 670000, Ulan-Ude, Buryat Republic, Russia

    A. M. Raigorodskii

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  1. A. M. Raigorodskii
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Correspondence to A. M. Raigorodskii.

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Translated by I. Ruzanova

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Raigorodskii, A.M. On Dividing Sets into Parts of Smaller Diameter. Dokl. Math. 102, 510–512 (2020). https://doi.org/10.1134/S1064562420060174

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  • DOI: https://doi.org/10.1134/S1064562420060174

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