排列函数和组合函数的性质与应用

Properties and Applications of Permutation and Combinatorial Functions

引入了排列函数与组合函数,推广了排列数与组合数的概念,获得了排列函数与组合函数的若干性质,得到了广义组合(或排列)数与普通组合(或排列)数的关系式.依据推广的二项式级数获得了一批新的组合恒等式.推导出了关于排列函数、组合函数的线性表示式、表示式系数的递推关系式和系数新公式,获得了等幂和的四个表示公式.

This paper introduces permutation and combination functions. It extends the conception of permutation and combinatorial numbers, obtains some properties of permutation and combination functions, and gets the relationship between generalized and ordinary combinatorial （permutation） numbers. Some new combinatorial identities are also obtained according to the generalized binomials, we derives the linear expression of about permutation and combination functions, the recurrence relation of the expressions＂ coefficients and the new coefficients formula, as well as four expression of sum of equal powers.