Patterns in treeshelves

Jean-Luc Baril (1) , Sergey Kirgizov (1) , Vincent Vajnovszki (1)

1 Le2i - Laboratoire d'Electronique, d'Informatique et d'Image [EA 7508]

We study the distribution and the popularity of left children on sets of treeshelves avoiding a pattern of size three. (Treeshelves are ordered binary increasing trees where every child is connected to its parent by a left or a right link.) The considered patterns are sub-treeshelves, and for each such a pattern we provide exponential generating function for the corresponding distribution and popularity. Finally, we present constructive bijections between treeshelves avoiding a pattern of size three and some classes of simpler combinatorial objects.

Mots clés: Binary increasing tree; Pattern; Statistic; Popularity; Bell/Euler(ian)/Lah number

Domaines: Informatique [cs]; Informatique [cs]; Mathématique discrète [cs.DM]

Jean-Luc Baril, Sergey Kirgizov, Vincent Vajnovszki. Patterns in treeshelves. Discrete Mathematics, 2017, 340 (12), pp.2946 - 2954. ⟨10.1016/j.disc.2017.07.021⟩. ⟨hal-01588383⟩