The existence and abundance of small bases of permutation groups

排列群小基的存在性和丰度

• 批准号: DE230100579
• 负责人: Dr Melissa Lee
• 金额: $ 31.4万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2023
• 资助国家: 澳大利亚
• 起止时间: 2023-01-09 至 2026-01-08
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE230100579
• 关键词: existence; abundance; small; bases; permutation

This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project include new methods to address enduring open problems in the study of bases, as well as novel applications of existing techniques. This should provide significant benefits, such as creating and strengthening international collaborations, and building on Australia’s reputation as a powerhouse of finite group theory.

这个项目旨在研究置换群的基础，这是对称性的数学形式化。基地是至关重要的编码和计算的群体在不同的科学领域。小基地是可取的效率，但很难找到。这个项目期望结合联合收割机技术，从代数和概率领域，以确定存在和丰富的基地。该项目的预期成果包括解决碱基研究中长期存在的开放性问题的新方法，以及现有技术的新应用。这应该会带来巨大的好处，比如建立和加强国际合作，以及建立澳大利亚作为有限群理论强国的声誉。