Statistics 简明教程
Statistics - Odd and Even Permutation
将 X 视为至少包含两个元素的有限集，然后 X 的排列可以分为两类大小相等的类别：偶排列和奇排列。
Consider X as a finite set of at least two elements then permutations of X can be divided into two category of equal size: even permutation and odd permutation.
Odd Permutation
奇排列是一组通过一组中奇数个两个元素交换所得的排列。它由 -1 的排列符号表示。对于一组 n 个数字（其中 n > 2），可能有 ${\frac{n!}{2}}$ 个排列。例如，对于 n = 1、2、3、4、5、…，可能的奇排列为 0、1、3、12、60 等
Odd permutation is a set of permutations obtained from odd number of two element swaps in a set. It is denoted by a permutation sumbol of -1. For a set of n numbers where n > 2, there are ${\frac {n!}{2}}$ permutations possible. For example, for n = 1, 2, 3, 4, 5, …, the odd permutations possible are 0, 1, 3, 12, 60 and so on…
Example
计算以下集合的奇排列：{1,2,3,4}。
Compute the odd permutation for the following set: {1,2,3,4}.
Solution:
Solution:
这里 n = 4，因此奇排列的总数量可能为 ${\frac {4!}{2} = \frac {24}{2} = 12}$。以下是生成奇排列的步骤。
Here n = 4, thus total no. of odd permutation possible are ${\frac {4!}{2} = \frac {24}{2} = 12}$. Following are the steps to generate odd permutations.
Even Permutation
偶排列是从集合中偶数个两个元素交换中得到的排列集合。它用 +1 的排列符号表示。对于 n 个数字的集合，其中 n > 2，有 ${\frac {n!}{2}}$ 种可能的排列。例如，对于 n = 1, 2, 3, 4, 5, …，可能的偶排列为 0, 1, 3, 12, 60，依此类推…
Even permutation is a set of permutations obtained from even number of two element swaps in a set. It is denoted by a permutation sumbol of +1. For a set of n numbers where n > 2, there are ${\frac {n!}{2}}$ permutations possible. For example, for n = 1, 2, 3, 4, 5, …, the even permutations possible are 0, 1, 3, 12, 60 and so on…
Example
计算以下集合的偶排列：{1,2,3,4}。
Compute the even permutation for the following set: {1,2,3,4}.
Solution:
Solution:
这里 n = 4，因此偶排列的总数量可能为 ${\frac {4!}{2} = \frac {24}{2} = 12}$。以下是生成偶排列的步骤。
Here n = 4, thus total no. of even permutation possible are ${\frac {4!}{2} = \frac {24}{2} = 12}$. Following are the steps to generate even permutations.