Near generalized balanced tournament designs with block sizes 4 and 5  

作　　者：SHAN XiuLing1, 2 1 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China 2 College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China 

出　　处：《Science China Mathematics》2009年第9期1927-1938,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10771051,10831002)

摘　　要：A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km+1,k,k-1)-BIBD defined on a (km+1)-set V . Its blocks can be arranged into an m×(km+1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V\{x} for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.A near generalized balanced tournament design, or an NGBTD(k,m) in short, is a (km + 1, k, k ? 1)-BIBD defined on a (km +1)-set V. Its blocks can be arranged into an m × (km + 1) array in such a way that (1) the blocks in every column of the array form a partial parallel class partitioning V[x] for some point x, and (2) every element of V is contained in precise k cells of each row. In this paper, we completely solve the existence of NGBTD(4,m) and almost completely solve the existence of NGBTD(5,m) with four exceptions.

关 键 词：near generalized balanced tournament designs frame generalized doubly resolvable packing constructions existence 05B05 

分 类 号：O157.2[理学—数学]