Juxtaposing Catalan Permutation Classes with Monotone Ones

This talk describes a clean and unified way to enumerate all juxtaposition classes of the form “Av(abc) next to Av(xy)”, where abc is a permutation of length three and xy is a permutation of length two. The main tools are Dyck paths, decorated by sequences of points, and context free grammars, used afterwards to enumerate these decorated Dyck paths. Juxtapositions are a simple special case of permutation grid classes. Grid classes found application mainly as tools to study the structure of other permutation classes. In [11], Vatter used the structural insights that monotone grid classes offer to classify growth rates of small permutation classes. Apart from enumerating permutation classes, several other applications of grid classes exist, among them [2, 1, 7, 8, 10, 12].