Applications of non-commutative symmetric functions to algebraic combinatorics

非交换对称函数在代数组合中的应用

• 批准号: 261951-2012
• 负责人: Zabrocki, Michael
• 金额: $ 1.82万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=571183
• 关键词: Applications; non; commutative; symmetric; functions

In the last 25 years mathematics research has gone into the development of certain non-commutative algebraic structures. While the initial motivation for studying these algebras was simply because of their mathematical beauty, they have been shown to have many unexpected applications. I have studied various types of non-commutative objects in my past research, usually simply to discover some of their most important properties and to generalize what is known for their commutative counterparts. My current research has been to tackle some important long standing problems of algebraic combinatorics and I have found that the techniques and results developed to study non-commutative algebra have lead to important breakthroughs on seeming unrelated problems.

在过去的25年里，数学研究已经进入了某些非交换代数结构的发展。 虽然研究这些代数的最初动机仅仅是因为它们的数学之美，但它们已经被证明有许多意想不到的应用。 在过去的研究中，我研究了各种类型的非对易对象，通常只是为了发现它们的一些最重要的性质，并概括出它们的对易对象。 我目前的研究一直是解决一些重要的长期存在的问题的代数组合，我发现，技术和成果开发的研究非交换代数导致重要的突破似乎无关的问题。