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 given which preclude most small variations in the hypotheses or conclusions of the two main results.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics