Non-Contiguous Pattern Avoidance in Binary Trees

Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn

Abstract


In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare these results to analogous work for contiguous tree patterns. Next, we give an explicit generating function that counts binary trees avoiding a single non-contiguous tree pattern according to number of leaves and show that there is exactly one Wilf class of k-leaf tree patterns for any positive integer k.  In addition, we give a bijection between between certain sets of pattern-avoiding trees and sets of pattern-avoiding permutations.  Finally, we enumerate binary trees that simultaneously avoid more than one tree pattern.

Keywords


Binary tree; Pattern avoidance

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