Complete mappings and orthogonal orthomorphisms of groups
主 讲 人 :冯弢 教授
活动时间:07月23日14时05分
地 点 :球友会D203报告厅
讲座内容:
A complete mapping of a finite group $G$ is a permutation $\phi: G\rightarrow G$ such that $x\mapsto x\phi(x)$ is also a permutation. A permutation $\theta:G\rightarrow G$ of a finite group $G$ is an orthomorphism of $G$ if the mapping $x\mapsto x^{-1}\theta(x)$ is also a permutation. Two orthomorphisms $\theta$ and $\phi$ of $G$ are orthogonal if the mapping $x\mapsto \theta(x)^{-1}\phi(x)$ is bijective. This talk provides a brief introduction to the existence of complete mappings and orthogonal orthomorphisms of groups, focusing on their algebraic and extremal aspects. Difference matrices have a close relationship with orthogonal orthomorphisms of groups. It will also give a survey on difference matrices and their related topics, such as orthogonal arrays and mutually orthogonal Latin squares.
主讲人介绍:
Tao Feng received the B.S. and Ph.D. degrees in mathematics from Beijing Jiaotong University, China, in 2003 and 2008, respectively. He is currently a Professor with the School of Mathematics and Statistics, Beijing Jiaotong University. His research interests include combinatorial design theory and coding theory.