Juxtaposing Catalan Permutation Classes with Monotone Ones

Robert Brignall, Jakub Sliačan


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.


Permutations; Juxtapositions; Dyck paths; Context-free grammars; Enumeration

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