拟阵族N的分裂子M(K_5)

Splitter M(K_5) of Matriod Family N

研究拟阵族N的分裂子M(K5)。先应用分裂子定理和拟阵的单扩张定理证明:若N={M:M是二元域拟阵且M不含有同构于F*7的拟阵},则F7是N的一个分裂子。据此证明了两个结论:1.若N={M:M是正则拟阵且M不含M(K3,3)-幼阵},则M(K5)是N的一个分裂子;2.M(K5)是EX(U2,4,F7,M(K3,3))和EX(U2,4,F7*,M(K3,3))的分裂子,并得到了这两个拟阵族的正则拟阵分解表示。

The splitter M（K5） of matroid family N is studied here. First by using splitter theorem and single-element extension theorem,a proposition is derived： if N= { M：M is a binary matriod andMdo not include matriod which is isomorphic to F7^＊} then F7 is a splieter of N. And then another two conclusion： 1. if.N= {M：M is a regular matriod and Mdo not includeM（K3,3） -minor} ,thenM（K5）is a splitter of N,2. M（K5） is a splitter of EX（U2,4,F7,M（K3,3））and EX（U2.4,F7^＊ ,M（K3,3））. And the representation of decomposition of regular matriod of two matriod family is gat.