On families of subsets with a forbidden subposet

  • Authors:

  • Jerrold r. Griggs;Linyuan Lu

  • Affiliations:

  • Department of mathematics, university of south carolina, columbia, sc 29208, usa (e-mail: griggs@math.sc.edu, lu@math.sc.edu);Department of mathematics, university of south carolina, columbia, sc 29208, usa (e-mail: griggs@math.sc.edu, lu@math.sc.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2009

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Abstract

Let ⊂ 2[n] be a family of subsets of {1, 2,. . ., n}. For any poset H, we say is H-free if does not contain any subposet isomorphic to H. Katona and others have investigated the behaviour of La(n, H), which denotes the maximum size of H-free families ⊂ 2[n]. Here we use a new approach, which is to apply methods from extremal graph theory and probability theory to identify new classes of posets H, for which La(n, H) can be determined asymptotically as n → ∞ for various posets H, including two-end-forks, up-down trees, and cycles C4k on two levels.