New Applications of Additive Combinatorics in Number Theory and Graph Theory

加法组合学在数论和图论中的新应用

• 批准号: DP140100118
• 负责人: Prof Igor Shparlinski
• 金额: $ 66.56万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2014
• 资助国家: 澳大利亚
• 起止时间: 2014-07-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP140100118
• 关键词: New; Applications; Additive; Combinatorics; Number

The project aims to advance significantly the interplay between additive combinatorics, number theory and graph theory. The project will use and advance methods and results of additive combinatorics and give new applications to such fundamental problems on Cayley graphs as connectivity, random walks, colouring and dominating sets. The significance of the project is ensured by its goal of advancing existing results and methods of additive combinatorics and also in finding their new applications that have long-lasting impact on paramount problems for Cayley graphs that underlie the architecture of crucial communication networks. Achieving progress on these problems and developing relevant methods of additive combinatorics will be the main outcomes.

该项目的目的是显着推进加法组合学，数论和图论之间的相互作用。该项目将使用和改进加法组合学的方法和结果，并为凯莱图的连通性、随机游动、着色和支配集等基本问题提供新的应用。该项目的重要性是确保其目标是推进现有的结果和方法的加法组合，并在寻找他们的新的应用程序，有长期持久的影响的首要问题的凯莱图的基础架构的关键通信网络。在这些问题上取得进展和发展相关的方法添加剂组合将是主要的成果。