Juxtaposing Catalan Permutation Classes with Monotone Ones

摘要

This paper enumerates all juxtaposition classes of the form "$mathrm{Av}(abc)$ next to $mathrm{Av}(xy)$", where $abc$ is a permutation of length three and $xy$ is a permutation of length two. We use Dyck paths decorated by sequences of points to represent elements from such a juxtaposition class. Context free grammars are then used to enumerate these decorated Dyck paths.