Iterating the Lehmer code on inversion sequences: Catalan fixed points and finite stabilization

Julian Allagan, Shanzhen Gao, Benjamin Testart

We study an operator $\Theta$ on finite integer sequences, where $\Theta (\sigma {)}_i$ counts the entries to the left of ${\sigma }_i$ that are strictly smaller than ${\sigma }_i$. This operator is a variant of the…