Lecture Content：

The problem of large Kirkman triple systems (LKTS) is one of the most famous open problems in the field of combinatorial design. The existence problem of LKTS, as summarized by Chang and Zhou, falls into two main categories: direct construction and recursive construction. Direct construction primarily utilizes profound mathematical tools from algebra, combinatorics, and probability theory, supplemented by computer searches to find key small orders. Many experts and scholars both domestically and internationally, such as Denniston, Wilson, Zhu, Kang, Chang, Ge, Ji, Zhou, etc., have conducted in-depth studies on direct construction. In the aspect of recursive construction, Denniston proposed a conditional construction from LKTS(v) to LKTS(3v); Zhang and Zhu extended it to an unconditional triple construction; in 2002, Lei presented a new recursive construction and existence result for the large Kirkman triple systems, reducing the complete resolution of LKTS to the construction of 30 specified pairs of OLKF and candlestick designs (RPCS) with decomposable and splittable properties; in 2007, Ji constructed LKTS(3v-3) using doubly decomposable Steiner quadruple systems SQS(v); in 2008, Ji and Lei extended the LR design, aiming to use LR(u) and LKTS(v) to construct LKTS(uv/3) by introducing RPICS for a new recursive construction method. This report, based on the aforementioned work, explores the application of parallel computing in direct construction and shares several computer-assisted search tools.

Speaker Introduction:

Ha Zheng, Doctor of Science, graduated from Beijing Jiaotong University. He is currently an Associate Professor at the College of Statistics and Data Science, Beijing Technology and Business University. Supported by the China Scholarship Council, he spent one year as a visiting scholar at Tohoku University in Japan and engaged in academic exchanges at the University of Tsukuba and Nagasaki University of Technology in Japan. His main research interests include combinatorial design and coding theory. He has completed one project funded by the National Natural Science Foundation of China (Youth Fund), participated in one major project of the National Natural Science Foundation of China, and published 6 SCI papers and 2 Chinese papers in professional journals.