如何将置换写成对合的乘积（以及为什么你可能会关心）
How to write a permutation as a product of involutions (and why you might care)
摘要：
众所周知，任何置换都可以写成两个对合的乘积。我们提供了一个明确的公式的方式来做到这一点，只取决于循环类型的置换。在许多情况下，这些数是在同一置换下计算的对称群的不可约特征标的绝对值的和，尽管除了所有圈都是相同大小的情况之外，我们没有很好的解释为什么会这样。
英文摘要：
It is well-known that any permutation can be written as a product of two involutions. We provide an explicit formula for the number of ways to do so, depending only on the cycle type of the permutation. In many cases, these numbers are sums of absolute values of irreducible characters of the symmetric group evaluated at the same permutation, although apart from the case where all cycles are the same size, we have no good explanation for why this should be so.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
