Juxtaposing Catalan permutation classes with monotone ones
Robert Brignall, Jakub Sliačan · Open Research Online - ORO (The Open University) · 2016
This paper enumerates 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. 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.