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Matematicheskie Zametki, 2019, Volume 106, Issue 3, Pages 387–394
DOI: https://doi.org/10.4213/mzm12099
(Mi mzm12099)
 

This article is cited in 2 scientific papers (total in 2 papers)

Systems of Representatives

K. D. Kovalenkoa, A. M. Raigorodskiibcde

a National Research University "Higher School of Economics", Moscow
b Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region
c Adyghe State University, Maikop
d Lomonosov Moscow State University
e Buryat State University, Institute for Mathematics and Informatics, Ulan-Ude
Full-text PDF (460 kB) Citations (2)
References:
Abstract: Lower and upper bounds are obtained for the size $\zeta(n,r,s,k)$ of a minimum system of common representatives for a system of families of $k$-element sets. By $\zeta(n,r,s,k)$ we mean the maximum (over all systems $\Sigma=\{M_1,\dots,M_r\}$ of sets $M_i$ consisting of at least $s$ subsets of $\{1,\dots,n\}$ of cardinality not exceeding $k$) of the minimum size of a system of common representatives of $\Sigma$. The obtained results generalize previous estimates of $\zeta(n,r,s,1)$.
Keywords: systems of common representatives, minimum systems of common representatives.
Received: 28.06.2018
Revised: 27.12.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 3, Pages 372–377
DOI: https://doi.org/10.1134/S0001434619090062
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: K. D. Kovalenko, A. M. Raigorodskii, “Systems of Representatives”, Mat. Zametki, 106:3 (2019), 387–394; Math. Notes, 106:3 (2019), 372–377
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12099
  • https://www.mathnet.ru/eng/mzm/v106/i3/p387
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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