Lower bounds for coverings of pairs by large blocks

Abstract

Letn≧k≧t be positive integers, andX—a set ofn elements. LetC(n, k, t) be the smallest integerm such that there existm k-tuples ofX B 1 B 2,...,B m with the property that everyt-tuple ofX is contained in at least oneB i . It is shown that in many cases the standard lower bound forC(n, k, 2) can be improved (k sufficiently large,n/k being fixed). Some exact values ofC(n, k, 2) are also obtained.

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Todorov, D.T. Lower bounds for coverings of pairs by large blocks. Combinatorica 9, 217–225 (1989). https://doi.org/10.1007/BF02124682

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Keywords

  • coverings
  • affine planes
  • projective planes

AMS subject classification code (1980)

  • 05 B 40