Kite-Group Divisible Designs

Group divisible design is an important concept and it is the foundation of many big question in the theory of Combinatorial Designs. During years of group divisible design's research, many results have been obtained. Especially, the content of {3}-GDD is already quite mature.In order to enlarge the range of application field of group divisible design, we will discuss a special kind of GDD which is called kite-GDD. Nowadays, necessary and sufficient conditions are given to the existence for kite-group divisible designs of type gtu1 by Haiyan Wang and Yanxun Chang in. The object we discuss in this paper is kite-group divisible designs of type ab1u. Being a special kind of GDD, kite-GDD's research will be done more smoothly in the light of normal GDD's method.There are four chapters in the thesis. The first chapter introduces the definition of kite-GDD and some known results in this field. The necessary conditions are given to the existence for kite-GDD of type ab1u and we demonstrate them. Also, we show some obvious results.In the second chapter, we provide some useful constructions for kite-GDD of type ab1u with the help of the study of {3}-GDD of the same type and kite-GDD of type gtu1. In addition, some designs with small parameters are solved by computer.In the third chapter, we will discuss the sufficient conditions of existences for kite-GDD of type ab1u. The main job is to find out all the designs which are under certain circumstances by the construction stated in the second chapter. For the other designs, we will rely on the computer or other constructions. In this paper, we prove that when b=3, the necessary conditions are also sufficient except for several possible designs.In the forth chapter, some discussions are given about kite-GDD of type a41u. And some further questions are put forward.