|
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
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
Citation:
K. D. Kovalenko, A. M. Raigorodskii, “Systems of Representatives”, Mat. Zametki, 106:3 (2019), 387–394; Math. Notes, 106:3 (2019), 372–377
Linking options:
https://www.mathnet.ru/eng/mzm12099https://doi.org/10.4213/mzm12099 https://www.mathnet.ru/eng/mzm/v106/i3/p387
|
Statistics & downloads: |
Abstract page: | 367 | Full-text PDF : | 83 | References: | 42 | First page: | 25 |
|