2022/04/20 by Étienne Bellin, Bellin, Etienne
Materials Science · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Quasicrystal Structures and Properties #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2204.09357
openalex publication_date 2022/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we study decreasing and increasing factorisations of the cycle, which are decompositions of the cycle (1~2… 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.