Construction of combinatorial objects using computers

使用计算机构建组合对象

• 批准号: 9373-2007
• 负责人: Lam, Clement
• 金额: $ 1.17万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=365158
• 关键词: Construction; combinatorial; objects; using; computers

The objective of my research is to determine the existence of combinatorial objects. After recently completing the search for the (22,8,4) balanced incomplete block design, I would like to work on some of the unsolved cased of partial geometries and their associated strongly regular graphs, especially those with less than 100 pointsThe basic technique for enumerating combinatorial objects is a computer-aided backtrack search. Since the unsolved cases on partial geometries are too big to be attacked  directly, I will use the technique of assuming an automorphism in order to reduce the size of the problem.These problems have been long outstanding. Their solution would lead to better  understanding of the object and to better computational methods.

我的研究目标是确定组合对象的存在性。在最近完成了对（22，8，4）平衡不完全区组设计的研究之后，我想研究一些未解的部分几何及其相关的强正则图，特别是那些少于100个点的图。由于部分几何的未解问题太大，无法直接解决，我将使用假设自同构的技术来缩小问题的规模。他们的解决方案将导致更好地理解对象和更好的计算方法。