摘要
一个确定的n元数码的排列,其道序数是不难求得的;反之,“已知逆序数,求有多少个n元置换”的问题要复杂得多。从最小数码的位置着手,充分利用逆序数是定数,给出一种解决此问题的新方法——最小数码定位法。此法通俗易懂,由此得到了逆序数为k(k=1,2,3……c_n^2)的n元数码的置换个数的一个递推公式:q_k(n)=1+q_1(n-l)+q_2(n-1)+q_3(n-1)+…+q_k(n-1)。
The converse ordinal number of the n - th numerals' fixed permutation is obtained easily while the problem is very difficult that how much is the n - th permutation when we know the converse ordinal number. This paper provides a new method to solve this problem that we call it the fixed position of the minimum number and we obtain a recurrence formula as follows;
where k is the converse ordinal number and n shows the n - th numerals.
