Kneser graphs are Hamiltonian for n≥3k
Journal of Combinatorial Theory Series B
Largest family without A ∪ B ⊆ C ∩ D
Journal of Combinatorial Theory Series A
Note: No four subsets forming an N
Journal of Combinatorial Theory Series A
On families of subsets with a forbidden subposet
Combinatorics, Probability and Computing
Lower bounds for constant weight codes
IEEE Transactions on Information Theory
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Let F be a family of subsets of an n-element set. Sperner's theorem says that if there is no inclusion among the members of F then the largest family under this condition is the one containing all @?n2@?-element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of F is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let P be a poset. The maximum size of a family F which does not contain P as a (not-necessarily induced) subposet is denoted by La(n,P). The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11-13, 2009], but it was somewhat updated in December 2010.