Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.dam.2011.08.021 | Discrete Applied Mathematics |
Keywords | Field | DocType |
sperner type theorem,largest family,certain generalization,banasthali university,present paper survey,certain configuration,family f,jubilee conference,element subsets,maximum size,discrete mathematics | Discrete mathematics,Family of sets,Combinatorics,Generalization,Sperner's lemma,Mathematics,Partially ordered set | Journal |
Volume | Issue | ISSN |
161 | 9 | 0166-218X |
Citations | PageRank | References |
0 | 0.34 | 16 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gyula O. H. Katona | 1 | 264 | 66.44 |