Two Combinatorial Covering Theorems

@article{Stein1974TwoCC,
  title={Two Combinatorial Covering Theorems},
  author={S. K. Stein},
  journal={J. Comb. Theory, Ser. A},
  year={1974},
  volume={16},
  pages={391-397}
}
This paper generalizes a measure-theoretic theorem of Rogers [4] and a number-theoretic theorem of Lorentz [3] in a combinatorial setting. The proofs are modelled after the original ones and the results are illustrated by coverings by translates of a subset of a group (or quasigroup). The first theorem asserts that if a family of subsets covers a finite set X, then some “fairly small” subfamily covers a “fairly large” subset of A’. The second asserts that given a family of subsets that covers a… CONTINUE READING

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