Lecture Content：

Separable Sets (PS) and Nearly Separable Sets (APS) are two important combinatorial configurations in combinatorial design theory, closely related to many other combinatorial structures such as Z-cyclic Whist tournament graphs, cyclic difference matrices, neighbor-free cyclic balanced sample designs, disjoint difference families, and light orthogonal codes. Due to the stringent requirements of separable and nearly separable sets, their existence issues remain largely unresolved to date. This report will summarize the research progress on separable and nearly separable sets and their connections to other combinatorial structures, presenting new construction methods for separable sets of prime squared order and several new results on the existence of these two types of combinatorial configurations.

Speaker Introduction:

Chang Yanxun is a second-level professor and doctoral supervisor at Beijing Jiaotong University. He is a recipient of the Second National University Young Teachers Award, honored as a middle-aged expert with significant contributions by the Ministry of Railways in 2000, and began receiving a national special allowance in 2004. He has been funded by the Fok Ying Tung Education Foundation's Sixth Higher Education Young Teachers Fund and has led 8 National Natural Science Foundation of China projects, including one key project. He has published 220 academic papers in the field of combinatorial mathematics and coding theory, 200 of which are included in the SCI. His work has won the First Prize for Scientific and Technological Progress in Hebei Province in 1991 and the Second Prize for Natural Sciences in the National University Science and Technology Award in 2001. He currently serves as an executive member of the National Committee of Combinatorial Mathematics and Graph Theory and the Beijing Mathematical Society.