Patterns in treeshelves

TL;DR

This paper analyzes the distribution and popularity of left children in treeshelves avoiding specific size-three patterns, providing generating functions and bijections to simpler objects.

Contribution

It introduces exponential generating functions for pattern-avoiding treeshelves and constructs bijections to simpler combinatorial structures.

Findings

Derived exponential generating functions for pattern-avoiding treeshelves

Established bijections with simpler combinatorial objects

Analyzed the distribution and popularity of left children

Abstract

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.