欢迎光临!
您现在所在的位置:首页 >> 通知公告 & 学术信息
科学研究
RESEARCH
The diagonal graphs and the Hall--Paige conjecture
时间  Datetime
2020-12-02 19:00 — 20:00
地点  Venue
Zoom APP(2)()
报告人  Speaker
Peter Cameron
单位  Affiliation
University of St Andrews
邀请人  Host
吴耀琨
备注  remarks
ZoomID: 979 115 40039; PW: 854187
报告摘要  Abstract

The diagonal groups are a family of permutation groups defined by a dimension (which we assume to be at least 2) and a group T, which may be finite or infinite and is not required to be simple.


The diagonal graphs are a family of graphs whose automorphism groups are the diagonal groups. They include as special cases two classical families of graphs, the Latin square graphs associated with the Cayley tables of groups, and the distance-transitive folded cubes. I will describe some properties of these graphs: spectrum, clique number, chromatic number, etc.


The determination of the chromatic number is not complete in all cases. Some of the results depend on the truth of the Hall--Paige conjecture (proved by Wilcox, Evans and Bray) on complete mappings of groups. I will describe this and explain how it is used in the analysis.


If time permits, I may describe the extension of the notion of complete mapping to semigroups, and some results on which semigroups admit complete mappings.


http://math.sjtu.edu.cn/conference/Bannai/2019/talk.php?20201202B