论文标题
周期的随机单调分解
Random monotone factorisations of the cycle
论文作者
论文摘要
在本文中，我们研究了周期的减少和增加的分解，这些周期是$ N-1 $转置的乘积满足单调性条件的循环$（1〜2 \ dots n）$的分解。我们阐明了具有$ n $顶点的这种分解和平面树之间的两次培训。这将使我们能够研究它们的某些组合特性，以及在层压板方面的几何表示，它们是单位磁盘中的非交叉线段。
In this article we study decreasing and increasing factorisations of the cycle, which are decompositions of the cycle $(1~2\dots n)$ into a product of $n-1$ transpositions satisfying monotonicity conditions. We explicit a bijection between such factorisations and plane trees with $n$ vertices. This will allow us to study some of their combinatorial properties, as well as a geometric representation in terms of laminations, which are non-crossing line segments in the unit disk.
