Random monotone factorisations of the cycle

Etienne Bellin

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arXiv · 2204.09357

Random monotone factorisations of the cycle

Etienne Bellin

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Abstract

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.

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Etienne Bellin. 2022-04-20. Random monotone factorisations of the cycle. https://arxiv.org/abs/2204.09357

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