Maximal sets of numbers not containing k + 1 pairwise coprimes and having divisors from a specified set of primes

  • Authors:

  • Rudolf Ahlswede;Vladimir Blinovsky

  • Affiliations:

  • Bielefeld University, Department of Mathematics, Bielefeld, Germany;Bielefeld University, Department of Mathematics, Bielefeld, Germany and Institute for Inform. Transm. Problems, Russian Acad. of Sci., Moscow, Russia

  • Venue:
  • Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
  • Year:
  • 2006

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Abstract

We find the formula for the cardinality of a maximal set of integers from {1,.....n} which does not contain k + 1 pairwise coprimes and each integer has a divisor from a specified set of r primes. We also find the explticit formula for this set when r = k + 1.