论文标题
虚拟排列和多符号
Virtual permutations and polymorhisms
论文作者
论文摘要
从对称组$ s_n $到较小的对称组$ s_ {n-1} $的天然地图，我们将排列的分解写入脱节周期的产物中，然后从此表达式中删除元素$ n $。因此，存在集合$ s_n $的$ \ mathfrak {s} $的倒数限制。 We equip $S_n$ with the uniform distribution (or more generally with an Ewens distribution) and get a structure of a measure space on $\mathfrak{S}$ (it is called 'virtual permutations' or 'Chinese restaurant process'), a double $S_\infty\times S_\infty $ of an infinite symmetric group acts on $\mathfrak{S}$ by left and right 'multiplications'.我们讨论了$ \ mathfrak {s} $的多态性（带有radon-nikodym衍生物的传播地图）的$ s_ \ infty \ times s_ \ infty $的关闭。我们获得了某些多态性的公式，特别是在关闭中心。表达方式是迪里奇分布的多个卷积的总和，求和集是dessins d'enfant的某些集合。
There is a natural map from a symmetric group $S_n$ to a smaller symmetric group $S_{n-1}$, we write a decomposition of a permutation into a product of disjoint cycles and remove the element $n$ from this expression. For this reason there exists the inverse limit $\mathfrak{S}$ of sets $S_n$. We equip $S_n$ with the uniform distribution (or more generally with an Ewens distribution) and get a structure of a measure space on $\mathfrak{S}$ (it is called 'virtual permutations' or 'Chinese restaurant process'), a double $S_\infty\times S_\infty $ of an infinite symmetric group acts on $\mathfrak{S}$ by left and right 'multiplications'. We discuss the closure of $S_\infty\times S_\infty $ in the semigroup of polymorphisms (spreading maps with spreaded Radon--Nikodym derivatives) of $\mathfrak{S}$. We get formulas for some polymorphisms, in particular for the center of the closure. Expressions are sums of multiple convolutions of Dirichlet distributions, summation sets are certain collections of dessins d'enfant.
