AAM  >> Vol. 4 No. 4 (November 2015)

    Prime Factorization of Sperner Theory

  • 全文下载: PDF(600KB) HTML   XML   PP.357-364   DOI: 10.12677/AAM.2015.44044  
  • 下载量: 1,361  浏览量: 3,779   国家自然科学基金支持



Sperner定理生成函数对称链Sperner Theory Generating Function Method Symmetric Chain



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.

张泰滺, 晁福刚, 任韩. Sperner理论的质因子分解问题[J]. 应用数学进展, 2015, 4(4): 357-364. http://dx.doi.org/10.12677/AAM.2015.44044


[1] Sperner, E. (1928) Ein Satz über Untermengen einer endlichen menge. Mathematische Zeitschrift, 27, 544-548.
[2] Dilworth, R.P. (1950) A Decomposition Theorem for Partially Or-dered Sets. Annals of Mathematics, 51, 161-166.
[3] Katona, G. (1975) Extremal Problems for Hypergraphs. In: Hall Jr., M. and van Lint, J.H., Eds., Combinatorics.
[4] Kleitman, D.J. and Sperner, J. (1973) Families of k-Independent Sets. Discrete mathematics, 6, 255-262.
[5] de Bruijn, N.G., van Ebbenhorst Tengbergen, C. and Kruyswijk, D. (1949) On the Set of Divisors of a Number. Nieuw Archief voor Wiskunde, 23, 191-193.
[6] Erdös, P., Ko, C. and Rado, R. (1961) Extremal Problems among Subsets of a Set. Quarterly Journal of Mathematics Oxford Se-ries, 12, 313-318.
[7] Greene, C., Katona, G. and Kleitman, D.J. (1976) Extensions of the EKR Theorem. Studies in Applied Mathematics, 55, 1-8.
[8] Lih, K.W. (1987) Problems in Finite Extremal Set Theory. Surikaisekikenkyusho-Kokyuroku, 607, 1-4.