在1/2Z^+中的(F-Z_1)-可流拟阵(M-Z_1)/Z_2  

(F-Z_1)-flowable Matroid(M-Z_1)/Z_2 in 1/2Z~

作　　者：吕国亮[1] 余保民[1] 

机构地区：[1]渭南师范学院数学与信息科学院,陕西渭南714000

出　　处：《数学的实践与认识》2013年第17期195-199,共5页Mathematics in Practice and Theory

基　　金：陕西省教育厅自然科学基金(12JK0866)

摘　　要：研究在1/2Z^+中的F-可流拟阵的幼阵的可流性.首先给出F-可流拟阵的充要条件及在1/2Z^+中是F-可流拟阵的定义.证明了辅助命题:若拟阵是无环元的,则它的每个元素都恰在k个余极小圈之中;对满足一定的条件的极小圈集合,成立最小极小圈集合的等式.设映射p′在幼阵中满足1/2Z^+中(F-Z_1)-可流拟阵的不等式,由p′定义p.证明p在拟阵中满足同样的不等式.由映射Φ满足是12/Z^+中F-可流拟阵的等式,可找到最小属于幼阵的极小圈,定义Φ′(C′)则可证明Φ′满足在1/2Z^+中是(F-Z_1)-可流的等式.即由在1/2Z^+中F-可流拟阵的充要条件,证明了幼阵在1/2Z^+中是(F-Z_1)-可流的.Some properties of minors of F-fiowable matroid in 1/2Z are investigated. The definition of F-flowable matroids in 1/2 Z＋ and necessary and sufficient conditions that a matriod is F-fiowable axe given. It is proved that if a matroid has no loop elements, then its every element is contained in the k minimum coircuits. For a set of minimum circuits satisfying certain conditions, there exist an equality of minimum sets of minimum circuits. For a function 1/2Z＋ ,defined p by p,it p＇ in minors satisfying inequality of （F - Z1）-flowable matroid in 1/2Z＋ , defined p by p＇, it is proved that p also satisfy the same inequality. From the function Ф which satisfying the equality of F-flowable matroids, the minimum circuits belongs to minors can be found, defined Ф＇ （C＇） and then, it can be showed that Ф＇ satisfy the （F - Z1）-flowable equality in 1/2Z＋. By the sufficient and necessary conditions of F-flowable in 1/2Z , the （F - Z1）-flowability of minors （M - Z1）/Z2 in 1/2Z is proved.

关 键 词：幼阵 F-可流拟阵 环 极小圈 

分 类 号：O151.21[理学—数学]