The partition method for poset-free families

Jerrold R. Griggs () and Wei-Tian Li ()
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Jerrold R. Griggs: University of South Carolina
Wei-Tian Li: Academia Sinica

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 8, 587-596

Abstract: Abstract 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 $\mathcal {B}$ .

Keywords: Combinatorics of partially ordered sets; Extremal set theory; Sperner theory; Lubell function (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10878-012-9476-9

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