报告题目：Orthogonal Steiner systems
报告人：周君灵教授（北京交通大学）
报告时间：2022年12月8日(周四) 上午11：00-12：00
腾讯会议：245-445-523
报告摘要：The research on orthogonal Steiner systems S(t,k,v) was initiated in 1968. For (t,k)=(2,3),(3,4), this corresponds to orthogonal Steiner triple systems (STSs) and Steiner quadruple systems (SQSs), respectively. The existence problem of a pair of orthogonal STSs or SQSs has been settled completely thirty years ago. However, for Steiner systems with t>2 and k> 4, only two small examples of orthogonal pairs were known to exist before this work. An infinite family of orthogonal Steiner systems S(3,5,v) is constructed here. In particular, the existence of a pair of orthogonal Steiner systems S(3,5,4^m+1) is established for any even m>1; in parallel a pair of orthogonal G-designs G((4^m+1)/5,5,5,3)$ is displayed for any odd m>2. The construction is based on the Steiner systems admitting 3-transitive automorphism groups supported by elementary symmetric polynomials. What's more, 50 mutually orthogonal Steiner systems S(5,8,24) are shown to exist.
邀请人：季利均