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}
}
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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