Algebraic combinatorics, matrix integrals and algebraic geometry

代数组合、矩阵积分和代数几何

• 批准号: 8907-2013
• 负责人: Goulden, Ian
• 金额: $ 2.48万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=592946
• 关键词: Algebraic; combinatorics; matrix; integrals; algebraic

Combinatorics is the study of arrangements of sets of finite objects and relationships between them. Research in combinatorics is centrally motivated by applications in other mathematical and physical sciences, and in engineering. Many such applications require only that one determine the number of objects in a set, called "counting" the set. In algebraic combinatorics we make extensive use of results and methods from algebra in this study. One of the most fundamental combinatorial objects is called a permutation, which reorders the elements of a finite set. A transposition is a very simple permutation, that simply interchanges the order of ("transposes") two of the elements. A product of permutations is obtained by successive reordering, and in algebra, the set of all permutations of a set with this product is called the symmetric group.

组合学是对有限对象及其之间关系的布置的研究。组合学的研究是由其他数学和物理科学以及工程学中的应用中的集中动机。许多此类应用程序仅要求一个确定一个集合中的对象数量，称为“计数”集合。在代数组合学中，我们在本研究中广泛使用代数的结果和方法。最基本的组合对象之一称为排列，它可以重新定位有限集的元素。换位是一个非常简单的置换，它只是互换了（“转移”）两个元素的顺序。置换的产物是通过连续的重新排序获得的，在代数中，该产品的所有置换量的集合称为对称组。