Extremal and probabilistic combinatorics

极值和概率组合学

• 批准号: 0701111
• 负责人: Laszlo Szekely
• 金额: $ 10.41万
• 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: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0701111&HistoricalAwards=false
• 关键词: Extremal; probabilistic; combinatorics

Drs. Lu and Szekely build on their previous work in combinatorics and graph theory and continue their research on problems related to graph visualization and graph drawing; random graph models; tree indices relevant for chemistry; models for biomolecular sequence evolution; and phylogeny reconstruction for species evolution. They also continue their long-running projects on fundamental questions in extremal set theory, extremal graph theory, and discrete geometry. The particular problems on which they work include* the further development of the theory of crossing numbers of graphs and of better graph drawing algorithms;* improving current bounds on Turan type extremal problem on hypergraphs, one of the toughest problems in extremal combinatorics;* improving our knowledge on Property B, where notoriously hard problems provide testing ground for new techniques;* extending current probabilistic tools in combinatorics to be applicable in a new or more general scenario;* work towards the unification of random graph models;* searching for new insights on antichains and on intersecting families of subsets;* reach a much better understanding of the Randic index, a concept of extremal graph theory that has been introduced and widely used in chemistry;* continuing the study of models of biomolecular sequence evolution and phylogenetic trees, of phylogenetic tree reconstruction algorithms, in particular the maximum likelihood method, and investigating the phylogeny problem in the setting of inverting random functions.There is increasing demand to understand ``optimal''extreme structures and ``typical'' random structures in discrete mathematics as this understanding often leads to new algorithms This project will investigate basic combinatorial questions about structures and will look for various applications of discrete mathematics in computer science, biology, and engineering.In addition, the proposers plan to continue their interdisciplinary collaborations with colleagues from engineering, biology, statistics, and computer science, and expect to solve some of their new problems.

博士。 Lu和Szekline基于他们以前在组合学和图形论方面的工作，并继续研究与图形可视化和图形图有关的问题；随机图模型；与化学相关的树指数；生物分子序列进化的模型；以及物种进化的系统发育重建。他们还继续在极端集理论，极端图理论和离散几何形状中的基本问题上进行长期的项目。它们工作的特定问题包括*跨越图形和更好的图形绘制算法的进一步发展；场景;*努力统一随机图模型；*寻找有关抗理和相交子集的新见解； likelihood method, and investigating the phylogeny problem in the setting of inverting random functions.There is increasing demand to understand ``optimal''extreme structures and ``typical'' random structures in discrete mathematics as this understanding often leads to new algorithms This project will investigate basic combinatorial questions about structures and will look for various applications of discrete mathematics in computer science, biology, and engineering.In此外，提议者计划继续与工程，生物学，统计学和计算机科学的同事继续跨学科的合作，并期望解决他们的一些新问题。