Morier-Genoud–Ovsienko unimodality conjecture for fence rank sequences

Let $F(\beta)$ be a fence and let $L(\beta)$ be the distributive lattice of lower order ideals of $F(\beta)$. Its rank sequence is $r(\beta):r_0,r_1,\ldots,r_n$, where $r_k$ is the number of elements of $L(\beta)$ at rank $k$. Morier-Genoud–Ovsienko's unimodality conjecture. For all $\beta$, the sequence $r(\beta)$ is unimodal. This conjecture was stated by Morier-Genoud and Ovsienko and is described in the source as having since been proved.