Juxtaposing Catalan Permutation Classes with Monotone Ones

  • Robert Brignall
  • Jakub Sliańćan
Keywords: Permutations, Juxtapositions, Dyck paths, Context-free grammars, Enumeration

Abstract

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.

Published
2017-04-13
Article Number
P2.11