Email this article Systems of Representatives
- Authors: Kovalenko K.D.1, Raigorodsky A.M.2,3,4,5
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Affiliations:
- Department of Mathematics
- Moscow Institute of Physics and Technology (State University)
- Lomonosov Moscow State University
- Caucasus Mathematical Center
- Institute for Mathematics and Informatics
- Issue: Vol 106, No 3-4 (2019)
- Pages: 372-377
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/152032
- DOI: https://doi.org/10.1134/S0001434619090062
- ID: 152032
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Abstract
Lower and upper bounds are obtained for the size ζ(n, r, s, k) of a minimum system of common representatives for a system of families of k-element sets. By ζ(n, r, s, k) wemean themaximum (over all systems Σ = {M1, …, Mr} of sets Mi 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 Σ. The obtained results generalize previous estimates of ζ(n, r, s, 1).
About the authors
K. D. Kovalenko
Department of Mathematics
Author for correspondence.
Email: kkd15@mail.ru
Russian Federation, Moscow, 119048
A. M. Raigorodsky
Moscow Institute of Physics and Technology (State University); Lomonosov Moscow State University; Caucasus Mathematical Center; Institute for Mathematics and Informatics
Author for correspondence.
Email: raigorodsky@yandex-team.ru
Russian Federation, Dolgoprudny, Moscow Oblast, 141701; Moscow, 119991; Maikop, 352700; Ulan-Ude, 670000
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