# Sperner理论的质因子分解问题Prime Factorization of Sperner Theory

DOI: 10.12677/AAM.2015.44044, PDF, HTML, XML, 下载: 1,736  浏览: 5,459  国家自然科学基金支持

Abstract: Sperner theory is one of the most marvelous branches in extremal set theory. It has many applica-tions in the field of operation research, computer science, hypergraph theory and so on. The original Sperner theorem is brilliant; however, there are quite a few constraints. Using number theory method, an alternative proof of Sperner theorem was obtained. As an application, we correspond subsets of Sperner to the roots of indefinite equations, simplifying the complex conformation of the set of solutions and getting nicer properties. The utilization of symmetric chain decomposition plays a great role in promotion, by establishing numerical correspondence between symmetric chain structure and integer collection. The symmetric chain decomposition method also supports the promotion. We build a connection between chains and collections.

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