Largest families without an \(r\)-fork

DOI10.1007/s11083-007-9067-zzbMath1127.05101OpenAlexW2084019246MaRDI QIDQ2464734

Annalisa De Bonis

Publication date: 17 December 2007

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11083-007-9067-z

zbMATH Keywords

Sperner type theoremExtremal set theoryExtremal problem for familiesFork

Mathematics Subject Classification ID

Extremal set theory (05D05)

Related Items (29)

Forbidden induced subposets of given height ⋮ Three layer \(Q _{2}\)-free families in the Boolean lattice ⋮ Set Families With a Forbidden Induced Subposet ⋮ Sperner type theorems with excluded subposets ⋮ Incomparable copies of a poset in the Boolean lattice. ⋮ Forbidden subposet problems with size restrictions ⋮ Forbidden Intersection Patterns in the Families of Subsets (Introducing a Method) ⋮ No four subsets forming an \(N\) ⋮ Exact forbidden subposet results using chain decompositions of the cycle ⋮ An upper bound on the size of diamond-free families of sets ⋮ The partition method for poset-free families ⋮ Diamond-free subsets in the linear lattices ⋮ Diamond-free families ⋮ Turán problems on non-uniform hypergraphs ⋮ On crown-free families of subsets ⋮ A note on the largest size of families of sets with a forbidden poset ⋮ Set families with forbidden subposets ⋮ On Families of Subsets With a Forbidden Subposet ⋮ Union-intersecting set systems ⋮ Bounds on maximal families of sets not containing three sets with \(A\cap B \subset C\), \(A \not\subset B\) ⋮ An improvement of the general bound on the largest family of subsets avoiding a subposet ⋮ Forbidden subposet problems for traces of set families ⋮ Families of subsets without a given poset in double chains and Boolean lattices ⋮ Ramsey numbers for partially-ordered sets ⋮ On forbidden poset problems in the linear lattice ⋮ A simple proof for a forbidden subposet problem ⋮ \(Q _{2}\)-free families in the Boolean lattice ⋮ Poset-free families and Lubell-boundedness ⋮ Abelian groups yield many large families for the diamond problem

Cites Work

• An extremal problem with excluded subposet in the Boolean lattice
• Largest family without \(A \cup B \subseteq C \cap D\)
• Logarithmic order of free distributive lattice
• Lower bounds for constant weight codes
• On generalized graphs
• A short proof of Sperner's lemma
• Generalization of Sperner’s Theorem on the Number of Subsets of a Finite Set
• On a lemma of Littlewood and Offord

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