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Mat. Zametki, 2019, Volume 106, Issue 3, Pages 387–394 (Mi mz12099)  

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

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 $\Sigma=\{M_1,…,M_r\}$ of sets $M_i$ consisting of at least $s$ subsets of $\{1,…,n\}$ 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00355
Ministry of Education and Science of the Russian Federation НШ-6760.2018.1

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm12099

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English version:
Mathematical Notes, 2019, 106:3, 372–377

Bibliographic databases:

UDC: 517
Received: 28.06.2018
Revised: 27.12.2018

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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\paper Systems of Representatives
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\jour Math. Notes
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