阶乘进制中位数码之和的k次幂的计算

Computation of k-th Powers of Digital Sums in the Factorial Base

为揭示整数在阶乘进制表示中的规律,研究了阶乘进制中一类位数码函数的性质。设w(m)为整数m(0≤m≤n!-1)在阶乘进制表示中的位数码之和。对任意和正整数x和任意给定的整数k≥0,并利用组合数学的方法给出了具有k次幂的一个精确计算公式。所得结果在编码、密码和计算复杂性理论中有很好的应用前景。

In order to find the rules of the representation for integers under the factorial base, a kind of digital sum function and its characteristics are studied. Let w （m） denote the digital sum of integer m m（0≤m≤n! -1） in the factorial base. For any positive integer x and any given integer k ≥0, a sharp calculating formula of the k - th power of this function is obtained by a mathematical combination method. These results are of perspective value in coding, cryptography and computation complexity theory.