Diamond-free families

  • Authors:

  • Jerrold R. Griggs;Wei-Tian Li;Linyuan Lu

  • Affiliations:

  • Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

  • Venue:
  • Journal of Combinatorial Theory Series A
  • Year:
  • 2012

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Abstract

Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of [n]:={1,...,n} that contains no (weak) subposet P. This problem has been studied intensively in recent years, and it is conjectured that @p(P):=lim"n"-"~La(n,P)/(n@?n2@?) exists for general posets P, and, moreover, it is an integer. For k=2 let D"k denote the k-diamond poset {A