# Minimal coverings and maximal packings of (k−1)-subsets by k-subsets

@article{Kuzyurin1977MinimalCA, title={Minimal coverings and maximal packings of (k−1)-subsets by k-subsets}, author={Nikolai Nikolaevich Kuzyurin}, journal={Mathematical notes of the Academy of Sciences of the USSR}, year={1977}, volume={21}, pages={316-320} }

- Published 1977
DOI:10.1007/BF01787658

AbstractThis paper studies the asymptotic behavior of functions M(n, k, k−1, λ) and m(n, k, k−1, λ), equal to the respective cardinalities of the minimal λ-covering and maximal λ-packing of all (k−1)-subsets of the n-element set of its k-subsets. It is shown that, if sequence k=k(n) is such that k(n)/n → 0 as η → ∞ then m(n, k, k−1, λ)∼λ.(k−1n).k1, and if
$$k\left( n \right)/\sqrt n \to 0$$
as n → ∞, thenM(n,k,k−1,λ)∼λ.(k−1 n).k−1. A consequence of these results is the validity of the Erdös… CONTINUE READING

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