Extremal and Probabilistic Combinatorics II

极值和概率组合学 II

• 批准号: 1000475
• 负责人: Laszlo Szekely
• 金额: $ 17.59万
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1000475&HistoricalAwards=false
• 关键词: Extremal; Probabilistic; Combinatorics; II

The investigators continue their work on graph drawing and crossing numbers, random graph models, phylogeny reconstruction, and on fundamental questions of extremal set and graph theory and discrete geometry. In particular, they will focus on Turan's hypergraph problem, on novel applications of the lopsided Lovasz Local Lemma, on Sperner type and extremal poset problems. They will use combinatorial and probabilistic techniques in phylogenetics and in the theory of complex network.Scientific and engineering breakthroughs in many fields have spurred the development of new theory and algorithms for discrete structures. There is increasing demand to understand "optimal" extreme structures and "typical" random structures in discrete mathematics. This project will investigate basic combinatorial questions about structures and will look for various applications of discrete mathematics in computer science, biology, and engineering.

研究人员继续进行图形绘图和交叉数字，随机图模型，系统发育重建以及极端设置和图理论和离散几何形状的基本问题。特别是，他们将重点介绍Turan的HyperGraph问题，这是在洛杉矶本地引理，斑点类型和极端POSET问题上的新型应用上。他们将在系统发育学和复杂网络理论中使用组合和概率技术。许多领域的科学和工程突破促使了开发新理论和离散结构算法。在离散数学中，需要越来越多地了解“最佳”极端结构和“典型”随机结构。该项目将研究有关结构的基本组合问题，并将寻找计算机科学，生物学和工程学中离散数学的各种应用。