用组合分析方法推导若干线性空间的维数

Derivation of the Dimentions of Some Linear Spaces by Methods of Combination and Analysis

在实数域R上 ,关于变元 χ1 ,χ2 ,… ,χk(k≥ 1 )的全体n次齐次多项式 ,≤n次多项式 ,n次齐次对称多次式 ,≤n次对称多项式 ,n次齐次轮换对称多项式 ,≤n次轮换对称多项式(均包含零多项式 ,n≥ 0 )分别组成线性空间 ,记为Un ,k、 Un,k、Vn ,k、 Vn ,k、Wn ,k、 Wn ,k。

In real number field R, all n -th power hoogeneous polynomials,≤\%n\%-th power polynomials, \%n\%-th power homogeneous symmetric polynomials, ≤\%n\%-th power symmetric polynomials, and \%n\%-th power homogeneous circular symmetric polynomials, as well as ≤ \%n\%-th circular symmetric polynomials ( each including0-th power polynomials, \%n\%≥0) of the variables\% X 1, X 2,…,X k (k≥1)\% respectively forms a linear space. This paper is to derivate their dimentions by methods of combination and analysis.