Perfect codes in Cayley graphs
报告题目(Title)：Perfect codes in Cayley graphs
报告人(Speaker)：周三明 教授（墨尔本大学）
地点(Place)：后主楼1328室
时间(Time)：2019年1月8日 下午4：00-5：00
邀请人(Inviter)：王恺顺 教授
报告摘要
Let G = (V, E) be a graph and t a positive integer. A perfect t-code in G is a subset C of V such that every vertex of G is at distance no more than t to exactly one vertex in C. Perfect t-codes in the Hamming graph H(n, q) are precisely q-ary perfect t-codes of length n in the classical setting, and those in the Cartesian product of a cycle of length q with itself n times are precisely q-ary perfect t-codes of length n under the Lee metric. Thus perfect codes in Cayley graphs are a generalization of perfect codes under the Hamming or Lee metric, and perfect 1-codes in Cayley graphs are closely related to tilings of the underlying groups. In this talk I will review some recent results on perfect codes in Cayley graphs, with an emphasis on perfect 1-codes.
主讲人简介
周三明，墨尔本大学数学与统计学院教授，研究领域包括代数图论及其应用、随机图过程、结构图论、网络优化等，发表论文 100 余篇。2003 年获国际组合数学及其应用学会 Kirkman 奖，2012-2015 年获澳大利亚研究委员会“未来研究员”（Future Fellowship）计划资助，为获此资助的少数几位组合学家之一。澳大利西亚组合数学会（Combinatorial Mathematics Society of Australasia）前任主席，Australasian J. Combinatorics 主编，J. Interconnection Networks (World Scientific) 和 Bulletin Malays. Math. Sci. Soc.(Springer) 编委。
