\(Q _{2}\)-free families in the Boolean lattice

DOI10.1007/s11083-011-9206-4zbMath1259.06001arXiv0912.5039OpenAlexW3100431406MaRDI QIDQ766139

Jacob Manske, Maria A. Axenovich, Ryan R. Martin

Publication date: 23 March 2012

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.5039

zbMATH Keywords

Boolean latticeforbidden posetextremal family

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Extremal set theory (05D05)

Related Items (12)

Three layer \(Q _{2}\)-free families in the Boolean lattice ⋮ Sperner type theorems with excluded subposets ⋮ A construction for Boolean cube Ramsey numbers ⋮ Exact forbidden subposet results using chain decompositions of the cycle ⋮ An upper bound on the size of diamond-free families of sets ⋮ Diamond-free subsets in the linear lattices ⋮ On crown-free families of subsets ⋮ Set families with forbidden subposets ⋮ Boolean algebras and Lubell functions ⋮ Upper bounds on the size of 4- and 6-cycle-free subgraphs of the hypercube ⋮ Existence thresholds and Ramsey properties of random posets ⋮ Abelian groups yield many large families for the diamond problem

Cites Work

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• Strong versions of Sperner's theorem
• An extremal problem with excluded subposet in the Boolean lattice
• Set families with a forbidden subposet
• No four subsets forming an \(N\)
• Largest families without an \(r\)-fork
• Largest family without \(A \cup B \subseteq C \cap D\)
• Logarithmic order of free distributive lattice
• On Families of Subsets With a Forbidden Subposet
• On generalized graphs
• A short proof of Sperner's lemma
• On a lemma of Littlewood and Offord

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