Stanley-Wilf Limits for Patterns in Rooted Labeled Forests

TL;DR

This paper extends the Stanley-Wilf conjecture to rooted forests, providing new analytic methods for pattern avoidance and computing bounds for forest Stanley-Wilf limits, with implications for future research.

Contribution

It proves a forest analogue of the Stanley-Wilf conjecture for single and multiple pattern avoidance, introducing analytic techniques for bounds and generalizations.

Findings

Proved forest Stanley-Wilf conjecture for single pattern avoidance

Developed analytic methods for computing lower bounds

Extended results to certain sets of patterns

Abstract

Building off recent work of Garg and Peng, we continue the investigation into classical and consecutive pattern avoidance in rooted forests. We prove a forest analogue of the Stanley-Wilf conjecture for avoiding a single pattern as well as certain other sets of patterns. Our techniques are analytic, easily generalizing to different types of pattern avoidance and allowing for computations of convergent lower bounds of the forest Stanley-Wilf limit in the cases covered by our result. We end with several open questions and directions for future research, including some on the limit distributions of certain statistics of pattern-avoiding forests.