题 目：Perfect codes in circulant graphs

报告人：周三明 教授（墨尔本大学）

Abstract : 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。曾获国际组合数学及其应用学会 Kirkman 奖。

时间： 1月10日（周四）晚上19：00-20:00

地点：565net必赢客户端本部教二楼 627 教室

联系人：杜少飞

欢迎全体师生积极参加！