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Mat. Zametki, 1970, Volume 7, Issue 3, Pages 319–323 (Mi mz9512)  

This article is cited in 12 scientific papers (total in 12 papers)

Realization of all distances in a decomposition of the space $R^n$ into $n+1$ parts

D. E. Raiskii

School for Working Youth, Moscow

Abstract: Let the sets $A_1, A_2, …, A_{n+1}$ form a covering of the $n$-dimensional euclidean space $R^n$ ($n>1$). Then among these sets can be found a set $A_i$ containing, for every $d>0$, a pair of points such that the distance between them is equal to $d$.

Full text: PDF file (585 kB)

English version:
Mathematical Notes, 1970, 7:3, 194–196

Bibliographic databases:

UDC: 513.83
Received: 10.12.1968

Citation: D. E. Raiskii, “Realization of all distances in a decomposition of the space $R^n$ into $n+1$ parts”, Mat. Zametki, 7:3 (1970), 319–323; Math. Notes, 7:3 (1970), 194–196

Citation in format AMSBIB
\Bibitem{Rai70}
\by D.~E.~Raiskii
\paper Realization of all distances in a decomposition of the space $R^n$ into $n+1$ parts
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 3
\pages 319--323
\mathnet{http://mi.mathnet.ru/mz9512}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=261446}
\zmath{https://zbmath.org/?q=an:0202.21702|0191.20506}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 3
\pages 194--196
\crossref{https://doi.org/10.1007/BF01093113}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. M. Raigorodskii, “On the chromatic number of a space”, Russian Math. Surveys, 55:2 (2000), 351–352  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. A. M. Raigorodskii, “Borsuk's problem and the chromatic numbers of some metric spaces”, Russian Math. Surveys, 56:1 (2001), 103–139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. S. A. Bogatyi, “Realization of Configurations and the Loewner Ellipsoid”, Math. Notes, 69:2 (2001), 149–157  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. A. M. Raigorodskii, “The Erdős–Hadwiger problem and the chromatic numbers of finite geometric graphs”, Sb. Math., 196:1 (2005), 115–146  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. A. M. Raigorodskii, “On the Borsuk and Erdös–Hadwiger numbers”, Math. Notes, 79:6 (2006), 854–863  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. L. L. Ivanov, “An estimate for the chromatic number of the space $\mathbb R^4$”, Russian Math. Surveys, 61:5 (2006), 984–986  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. O. I. Rubanov, “Chromatic Numbers of 3-Dimensional Distance Graphs Containing No Tetrahedra”, Math. Notes, 82:5 (2007), 718–721  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. V. O. Manturov, “On the chromatic numbers of integer and rational lattices”, Journal of Mathematical Sciences, 214:5 (2016), 687–698  mathnet  crossref
    9. A. E. Zvonarev, A. M. Raigorodskii, D. V. Samirov, A. A. Kharlamova, “On the chromatic number of a space with forbidden equilateral triangle”, Sb. Math., 205:9 (2014), 1310–1333  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. A. V. Bobu, O. A. Kostina, A. E. Kupriyanov, “Independence numbers and chromatic numbers of some distance graphs”, Problems Inform. Transmission, 51:2 (2015), 165–176  mathnet  crossref  isi  elib
    11. A. Ya. Kanel-Belov, V. A. Voronov, D. D. Cherkashin, “On the chromatic number of infinitesimal plane layer”, St. Petersburg Math. J., 29:5 (2018), 761–775  mathnet  crossref  mathscinet  isi  elib
    12. E. S. Gorskaya, I. M. Mitricheva, “The chromatic number of the space $(\mathbb R^n, l_1)$”, Sb. Math., 209:10 (2018), 1445–1462  mathnet  crossref  crossref  isi  elib
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