Mathematical Sciences: Algebraic Combinatorics: Permutations and Partially Ordered Sets

数学科学：代数组合：排列和偏序集

• 批准号: 9208283
• 负责人: Curtis Greene
• 金额: $ 10.06万
• 依托单位: Haverford College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-01 至 1995-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208283&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Combinatorics; Permutations

This award supports the research of Professor C. Greene to work in combinatorics. He intends to investigate partially ordered sets, representations of the symmetric group and tableaux. In particular, he intends to work on Young's seminormal representation of the symmetric group, Mobius functions on planar lattices, balanced tableaux, the lattice of shuffles and a conjecture of D. Jackson on lattice-determinants. The research is in the general area of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be organized. And, so it is extremely important to modern communications, for example the design of large networks as in telephone systems and the design of algorithms in computer science.

该奖项支持格林教授在组合学方面的研究。他打算研究部分有序集合、对称群的表示和场景。特别是，他打算研究杨的对称群的半正规表示，平面格上的莫比乌斯函数，平衡表，洗牌的格和D. Jackson关于格行列式的猜想。这项研究是在组合学的一般领域。组合学试图找到有效的方法来研究如何组织离散的对象集合。因此，它对现代通信非常重要，例如电话系统中大型网络的设计以及计算机科学中算法的设计。