More Large Sets of Resolvable MTS and DTS with Even Orders  

作　　者：Qing-de Kang Rong-jia Xu 

机构地区：[1]Institute of Mathematics, Hebei Normal University, Shijiazhuang 050016, China [2]Qinhuangdao Radio and TV University, Qinhuangdao 066001, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第2期233-252,共20页应用数学学报（英文版）

基　　金：the National Natural Science Foundation of China(No.10671055);Natural Science Foundation of Hebei(No.A2007000230)

摘　　要：In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.In this paper, we first introduce a special structure that allows us to construct a large set of resolvable Mendelsohn triple systems of orders 2q ＋ 2, or LRMTS（2q ＋ 2）, where q = 6t ＋ 5 is a prime power. Using a computer, we find examples of such structure for t C T = {0, 1, 2, 3, 4, 6, 7, 8, 9, 14, 16, 18, 20, 22, 24}. Furthermore, by a method we introduced in [13], large set of resolvable directed triple systems with the same orders are obtained too. Finally, by the tripling construction and product construction for LRMTS and LRDTS introduced in [2, 20, 21], and by the new results for LR-design in [8], we obtain the existence for LRMTS（v）and LRDTS（v）, where v = 12（t ＋ 1） mi≥0（2.7mi＋1）mi≥0（2.13ni＋1）and t∈T,which provides more infinite family for LRMTS and LRDTS of even orders.

关 键 词：Large set resolvable Mendelsohn triple system tripling construction resolvable directed triple system 

分 类 号：O157.6[理学—数学]