Work

Non-Contiguous Pattern Avoidance in Binary Trees

Year: 2012

Type: article

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.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/2099

Authors: Michael Dairyko, Lara Pudwell, Samantha Tyner, Casey Wynn

Institutions: Pomona College, Valparaiso University, Augustana University, Augustana College, Hendrix College

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Science Foundation

Award: Valparaiso Experience in Research by Undergraduate Mathematicians