拟阵的单扩张与分裂子的确定  

Single-element Extension of a Matriod and Determination of a Splitter

作　　者：吕国亮[1] 赵小鹏[1] 

机构地区：[1]渭南师范学院数学与信息科学系,渭南714000

出　　处：《科学技术与工程》2010年第9期2045-2048,共4页Science Technology and Engineering

摘　　要：研究用拟阵的单扩张M′=M+Ee来确定拟阵族N的分裂子的方法。首先证明了M′=M+Eer(M′)=r(M),并且对每个M中包含e的极小圈C,都有|C|=r(M)+1。讨论了拟阵AG(3,2)和拟阵P6的性质。给出了拟阵M具有性质(P)的充要条件。由以上结果用两种方法证明了:若M=AG(3,2),E=E(M),令N={M:M不含有幼阵同构于w3或P6},则M+Ee是N的一个分裂子。The determination of splitter of a matriod family N by the single-element extension M＇=M＋E^e of a matriod is sdudied. First M＇=M＋E^e←→ r（M＇）=r（M） is goten,and then ｜C｜=r（M）＋1 for every circuit C of M which include e. The properties of matriod AG（3,2）and matriod P6 are discussed. Some necessary and sufficient conditions of matriod M with property （P） is proposed. With the result above,by two ways,that if M=AG（3,2）,E=E（M）,let N={M：M not include minor which is isomorphic to w^3 or P6} is proved,then M＋E^e is a splitter of N.

关 键 词：单扩张 分裂子 模割 包围z 可F-线性表示 

分 类 号：O157.5[理学—数学]