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Perfect codes in Cayley graphs
发布时间: 2019-01-08     10:59   【返回上一页】 发布人:周三明


 

代数组合论学术报告

 

 

 

 

报告题目Perfect codes in Cayley graphs

 

报告人:周三明 教授(墨尔本大学)

 

时间地点:2019年1月8日 下午4:00-5:00,后主楼1328室

 

邀请人: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.

 

个人简介: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。