RUI: Characterization Problems, Outer Models, and Forcing

RUI：表征问题、外部模型和强迫

• 批准号: 0100612
• 负责人: Maurice Stanley
• 金额: $ 10.1万
• 依托单位: San Jose State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-06-01 至 2004-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100612&HistoricalAwards=false
• 关键词: RUI; Characterization; Problems; Outer; Models

ABSTRACTThe investigator will continue his research in enumerative andalgebraic combinatorics. He feels that there are many opportunitiesfor strengthening the myriad connections between combinatorics andother branches of mathematics. He will investigate how recentbreakthroughs in the theory of total positivity can be applied to openproblems concerning such topics as counting faces in cubical polytopesand counting stable sets in clawfree graphs. The investigator willalso continue his research on the combinatorial properties of convexpolytopes that have arisen in such areas as statistical inference andthe representation theory of semisimple Lie algebras. In particular,he will investigate further some convex polytopes related to Kostant'spartition function. He will in addition pursue a number ofmiscellaneous problems arising in the work of Kac, Kontsevich,Varchenko, and others.The field of combinatorics was first systematically investigated inthe 1960's and only recently has reached a high level of maturity. Itis an area of mathematics that has close connections with many othersubjects, ranging from algebra, geometry, and statistics withinmathematics, andcomputer science, high-energy physics, chemistry, andmost recently biology without. The investigator's primary interest isthe development of connections between combinatorics and other areasof mathematics. He will investigate a number of problems that wouldcontinue the development of the connections between combinatorics andother branches of mathematics and that would lead to the developmentof tools that could be used by scientists outside of mathematics.

研究者将继续他在计数和代数组合学方面的研究。他认为有很多机会来加强组合数学和其他数学分支之间的联系。他将研究如何在最近的突破理论的总积极性可以应用到开放的问题，如计数面等主题的立方多面体和计数稳定集无爪图。调查员也将继续他的研究组合性质的凸多面体已经出现在这些领域的统计推断和表示理论的半单李代数。特别地，他将进一步研究与Kostant的配分函数有关的凸多面体。 他还将继续研究卡茨、孔采维奇、瓦尔琴科等人工作中出现的一些杂项问题。组合数学领域首次系统地研究是在20世纪60年代，直到最近才达到高度成熟。这是一个与许多其他学科有着密切联系的数学领域，从数学中的代数、几何和统计，到计算机科学、高能物理、化学，以及最近的生物学。研究者的主要兴趣是发展组合学和其他数学领域之间的联系。他将研究一些问题，这些问题将继续发展组合数学和其他数学分支之间的联系，并将导致数学之外的科学家可以使用的工具的发展。