Journal of Combinatorial Optimization

, Volume 25, Issue 4, pp 587–596 | Cite as

The partition method for poset-free families

  • Jerrold R. Griggs
  • Wei-Tian Li


Given a finite poset P, let \({\rm La}(n,P)\) denote the largest size of a family of subsets of an n-set that does not contain P as a (weak) subposet. We employ a combinatorial method, using partitions of the collection of all full chains of subsets of the n-set, to give simpler new proofs of the known asymptotic behavior of \({\rm La}(n,P)\), as n, when P is the r-fork \(\mathcal {V}_{r}\), the four-element N poset \(\mathcal {N}\), and the four-element butterfly-poset \(\mathcal {B}\).


Combinatorics of partially ordered sets Extremal set theory Sperner theory Lubell function 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of South CarolinaColumbiaUSA
  2. 2.Institute of MathematicsAcademia SinicaTaipeiTaiwan

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