Non-Contiguous Pattern Avoidance in Binary Trees

Details Non-Contiguous Pattern Avoidance in Binary Trees Non-Contiguous Pattern Avoidance in Binary Trees

2012-03-05

arxiv.org/abs/1203.0795v1

Mathematics

Combinatorics

21 pages, 2 figures, 2 tables

Scientific paper

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. In addition, we enumerate binary trees that simultaneously avoid more than one tree pattern. Finally, we explore connections between pattern-avoiding trees and pattern-avoiding permutations.

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