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Probl. Peredachi Inf., 2017, Volume 53, Issue 4, Pages 16–42 (Mi ppi2250)  

This article is cited in 7 scientific papers (total in 7 papers)

Coding Theory

On the number of edges of a uniform hypergraph with a range of allowed intersections

A. V. Bobua, A. E. Kupriyanova, A. M. Raigorodskiibac

a Department of Mathematical Statistics and Random Processes, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
b Department of Innovation and High Technology, Moscow Institute of Physics and Technology (State University), Moscow, Russia
c Institute of Mathematics and Computer Science, Buryat State University, Ulan-Ude, Russia

Abstract: We study the quantity $p(n,k,t_1,t_2)$ equal to the maximum number of edges in a $k$-uniform hypergraph having the property that all cardinalities of pairwise intersections of edges lie in the interval $[t_1,t_2]$. We present previously known upper and lower bounds on this quantity and analyze their interrelations. We obtain new bounds on $p(n,k,t_1,t_2)$ and consider their possible applications in combinatorial geometry problems. For some values of the parameters we explicitly evaluate the quantity in question. We also give a new bound on the size of a constant-weight error-correcting code.

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English version:
Problems of Information Transmission, 2017, 53:4, 319–342

Bibliographic databases:

UDC: 621.391.1+519.1
Received: 27.01.2017
Revised: 25.06.2017

Citation: A. V. Bobu, A. E. Kupriyanov, A. M. Raigorodskii, “On the number of edges of a uniform hypergraph with a range of allowed intersections”, Probl. Peredachi Inf., 53:4 (2017), 16–42; Problems Inform. Transmission, 53:4 (2017), 319–342

Citation in format AMSBIB
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\by A.~V.~Bobu, A.~E.~Kupriyanov, A.~M.~Raigorodskii
\paper On the number of edges of a~uniform hypergraph with a~range of allowed intersections
\jour Probl. Peredachi Inf.
\yr 2017
\vol 53
\issue 4
\pages 16--42
\mathnet{http://mi.mathnet.ru/ppi2250}
\elib{http://elibrary.ru/item.asp?id=30729589}
\transl
\jour Problems Inform. Transmission
\yr 2017
\vol 53
\issue 4
\pages 319--342
\crossref{https://doi.org/10.1134/S0032946017040020}
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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. Sagdeev, “On the Frankl–Rödl theorem”, Izv. Math., 82:6 (2018), 1196–1224  mathnet  crossref  crossref  adsnasa  isi  elib
    2. A. A. Sagdeev, “Exponentially Ramsey sets”, Problems Inform. Transmission, 54:4 (2018), 372–396  mathnet  crossref  isi  elib
    3. D. A. Zakharov, A. M. Raigorodskii, “Clique Chromatic Numbers of Intersection Graphs”, Math. Notes, 105:1 (2019), 137–139  mathnet  crossref  crossref  isi  elib
    4. A. V. Bobu, A. E. Kupriyanov, “Refinement of Lower Bounds of the Chromatic Number of a Space with Forbidden One-Color Triangles”, Math. Notes, 105:3 (2019), 329–341  mathnet  crossref  crossref  isi  elib
    5. Ph. A. Pushnyakov, “The Number of Edges in Induced Subgraphs of Some Distance Graphs”, Math. Notes, 105:4 (2019), 582–591  mathnet  crossref  crossref  isi  elib
    6. D. A. Zakharov, “O khromaticheskikh chislakh nekotorykh distantsionnykh grafov”, Matem. zametki, 107:2 (2020), 210–220  mathnet  crossref
    7. F. A. Pushnyakov, A. M. Raigorodskii, “Otsenka chisla reber v osobykh podgrafakh nekotorogo distantsionnogo grafa”, Matem. zametki, 107:2 (2020), 286–298  mathnet  crossref
  • Проблемы передачи информации Problems of Information Transmission
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