阶为偶数的幻三元系构造方法的研究  

Research on the Construction Method of the Magic Triple System with Even Order

作　　者：袁文娜 赵红涛[1] YUAN Wen-na;ZHAO Hong-tao(College of Mathematics,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《数学的实践与认识》2024年第5期223-228,共6页Mathematics in Practice and Theory

摘　　要：在幻三元系已有定理的基础上给出了偶数情况下的分类,进而通过可分解设计思想进行1-因子分解,并充分利用平衡不完全区组设计、可分解设计、柯克曼三元系等辅助设计构造了除α=12m-8外所有阶为偶数,k=2,λ<α2情况的幻三元系(α,β,λ,k)-MTS.On the basis of the existing theorem of the magic triple system,the classification of even-number cases is given,and then the 1-factor decomposition is carried out by resolvable design idea.(α,β,λ,k)-MTS with even order,α=12m-8,k=2,λ<α-2 is constructed by macking full use of auxiliary design such as balanced incomplete block design,resolvable design,Kirkman triple system.

关 键 词：1-因子分解 可分解设计 平衡不完全区组设计 柯克曼三元系 幻三元系 

分 类 号：O157.5[理学—数学]