论文标题
随机均匀最小因素化的程度
Degrees in random uniform minimal factorizations
论文作者
论文摘要
我们对$ n $ cycle的随机均匀分解感兴趣，这些因素是$ N-1 $转换的产品的$（1〜2 \ dots n）$的因素化。我们的主要结果是一个明确的公式，即1和2在均匀的最小分解中显示给定次数的联合概率。为此，我们将徒与Cayley树结合在一起，以及对多元生成功能的明确计算。
We are interested in random uniform minimal factorizations of the $n$-cycle which are factorizations of $(1~2\dots n)$ into a product of $n-1$ transpositions. Our main result is an explicit formula for the joint probability that 1 and 2 appear a given number of times in a uniform minimal factorization. For this purpose, we combine bijections with Cayley trees together with explicit computations of multivariate generating functions.
