【摘要】 文中符号a(m,r)表示min{n:对于二元域上n维向量空间V(n)的任意r-着色都存在单色m维仿射空间},T.C.Brown给出了a(m,r)的某些上界,本文改进了这些结果,主要得到同时,还对某些特殊情况给出a(m,r)的值。如:a(2,2)=4,a(2,3)=4,a(2,4)=5等。更多还原

【Abstract】 In this paper, the notation a(m, r) denotes min{n, for every r-coloring of n-dimensional Vector space V(n)over the binary fields, there exists a monochromatic affine m-space}. Some upper bounds of a(m, r) have been obtained by Brown. In this paper we improve these results, and obtain the following main resultsIn the meantime, we give the valus of a(m, r) for some special cases, e. g. a(2, 2)=4, a(2, 3)=4, a(2, 4)=5.etc.更多还原