Sperner定理在压缩滤子上的推广研究
Extension Research of Sperner’s Theorem on Compressed Filters
DOI: 10.12677/AAM.2021.108293, PDF,   
作者: 刘相芯, 尚 宇：辽宁师范大学数学学院，辽宁 大连
关键词: Sperner集族；凸集；理想；滤子；压缩滤子；Sperner Family； Convex Family； Ideal； Filter； Compressed Filter
摘要: 令Bn为[n]={1,2,...,n}的所有子集按包含关系构成的偏序集。Sperner定理说明Bn中最大的Sperner集族的密度为。本文研究Sperner定理在凸集上的推广，并证明Sperner定理在压缩滤子上成立。
Abstract: Let [n]={1,2,...,n} and Bn={A,A⊆[n]}. Sperner theorem states that the density of the largest Sperner family in Bn is . Our paper focuses on the extension of Sperner theorem on convex family and proves that Sperner theorem is valid on compressed filters.
文章引用：刘相芯, 尚宇. Sperner定理在压缩滤子上的推广研究[J]. 应用数学进展, 2021, 10(8): 2816-2821. https://doi.org/10.12677/AAM.2021.108293

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