三元系的大集与超大集  

Large sets and overlarge sets of triple systems

作　　者：康庆德[1] 袁兰党[2] 

机构地区：[1]河北师范大学数学研究所,石家庄050024 [2]河北师范大学数学与信息科学学院,石家庄050024

出　　处：《中国科学：数学》2017年第11期1409-1422,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11171089)资助项目

摘　　要：组合设计中的大集问题有着悠久的历史和重要的应用.但囿于其难度,长期进展很慢.近30年来,在一些新方法推动下,大集研究呈现了良好的态势.本文综述了几类经典三元系设计的大集及超大集的研究进展,同时给出了存在2.13~n+1阶Kirkman三元系超大集和3.5~n阶可分解Mendelsohn三元系超大集的新结果.The large set problem in the combinatorial design theory has a long history and important appli- cations. The related research work had been quite slow in making progress for a long period of time due to its sophistication. Being benefited and motivated by some new methodology the research in the large set problem has taken on a promising posture in recent thirty years. In this paper, we give a comprehensive summary about the development of large sets and overlarge sets for some types of classical triple systems. In addition, we obtain new results that there exist an OLKTS（2 · 13n ＋ 1） and an OLRMTS（3· 5^n）, where n≥ 0.

关 键 词：组合设计 Steiner三元系 KIRKMAN三元系 MENDELSOHN三元系 大集 超大集 

分 类 号：O157.2[理学—数学]