On a Conjecture on the Sperner Property
β Scribed by Zha, Xiaoya
- Book ID
- 122472071
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 365 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0195-6698
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let F be a nonempty collection of subsets of [n] = {1, 2, . . . , n}, each having cardinality t. Denote by P F the poset consisting of all subsets of [n] which contain at least one member of F , ordered by set-theoretic inclusion. In 1980, K. W. Lih conjectured that P F has the Sperner property for
## Dedicated to E. Corominas Motivated by the problem of estimating the age (in generations) of a population that evolves according to the Galton-Watson process, we consider graded partially ordered sets on which a probability measure is defined. By looking at the antichain of maximal probability,
Sufficient conditions are established for the product of two ranked partially ordered sets to have the Sperner property. As a consequence, it is shown that the class of strongly Sperner rank-unimodal rank-symmetric partially ordered sets is closed under the operation of product. Counterexamples are