The existence and abundance of small bases of permutation groups

这个项目旨在研究置换群的基，这是对称的数学形式化。在不同的科学领域，碱基对于分组编码和计算是至关重要的。为了提高效率，小基地是可取的，但很难找到。这个项目希望结合代数和概率领域的技术来确定基的存在和丰度。该项目的预期成果包括解决基地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。这应该会带来显著的好处，比如创建和加强国际合作，并建立澳大利亚作为有限群论强国的声誉。

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.